3.7 Evaluating Trig Functions To properly evaluate trig ratios on our calculator, we need to make sure we are in the right.
Download ReportTranscript 3.7 Evaluating Trig Functions To properly evaluate trig ratios on our calculator, we need to make sure we are in the right.
Slide 1
3.7 Evaluating Trig Functions
To properly evaluate trig ratios on our calculator, we need to
make sure we are in the right MODE – Degrees or Radians
If it has a degree symbol put in Degree Mode
If no symbol at all put in Radian Mode
Ex 1) Find the value (round to 4 dec. places)
a) cos 275°
(degree mode)
cos 275° = 0.0872
b) sin (–1.4π) (radian mode) sin (–1.4π) = 0.9511
c) tan 2
(radian mode) tan 2 = –2.1850
To evaluate ratios when given Deg-Min-Sec, either convert to just
degrees or use the °, ʹ, ʺ buttons on your calculator
To evaluate csc x, sec x & cot x, you will need to utilize the fact that
they are reciprocal functions
1
1
1
Remember:
csc x
sec x
cot x
sin x
cos x
tan x
Ex 2) Find the value (round to 4 dec. places)
a) sec 146°
(degree mode)
1
sec146
1.2062
cos146
b) cot 39° 52ʹ 15ʺ
(degree mode)
1
cot 395215
1.1972
tan 395215
OR
cot 39.8708
1
tan 39.8708
1.1972
We can also solve for an angle (in degrees or radians) if we know the
ratio. Use the inverse trig functions (sin–1θ, cos–1θ, tan–1θ)
*Often these problems can have more than 1 answer – you need to
think and draw a sketch!!
Ex 3) Find the values of θ where 0° ≤ θ < 360° (round to
(degree mode!!)
nearest tenth)
a) sin θ = 0.7193
θ
θ = sin–1(0.7193)
θ = 46.0° AND…sinθ is (+) in QI
θ
& QII
180 – 46 = 134.0°
θ = 46.0° and 134.0°
Ex 3) Find the values of θ where 0° ≤ θ < 360° (round to
(degree mode!!)
nearest tenth)
b) tan θ = –0.2309
θ = tan–1(–0.2309)
θ = –13.0°
tanθ is (–) in QIV & QII
13.0°
–13.0°
180 – 13 = 167.0°
360 – 13 = 347.0°
θ = 167.0° and 347.0°
Ex 4) Find the values of θ where 0 ≤ θ < 2π (round to nearest
(radian mode!!)
hundredth)
a) cos θ = –0.4611
θ = cos–1(–0.4611)
2.05
θ = 2.05
–2.05
cosθ is (–) in QII
& QIII
θ = 2.05 rad and 4.23 rad
2π – 2.05 = 4.23
Ex 4) Find the values of θ where 0 ≤ θ < 2π (round to nearest
hundredth)
(radian mode!!)
b) sec θ = 8.2986
1
8.2986
cos
1
cos
8.2986
1
1
cos
8.2986
1.45
1.45
–1.45
cosθ is (+) in QI
θ = 1.45 rad and 4.83 rad
& QIV
2π – 1.45 = 4.83
Homework
#307 Pg 163 #1–41 odd, 44
Slide 2
3.7 Evaluating Trig Functions
To properly evaluate trig ratios on our calculator, we need to
make sure we are in the right MODE – Degrees or Radians
If it has a degree symbol put in Degree Mode
If no symbol at all put in Radian Mode
Ex 1) Find the value (round to 4 dec. places)
a) cos 275°
(degree mode)
cos 275° = 0.0872
b) sin (–1.4π) (radian mode) sin (–1.4π) = 0.9511
c) tan 2
(radian mode) tan 2 = –2.1850
To evaluate ratios when given Deg-Min-Sec, either convert to just
degrees or use the °, ʹ, ʺ buttons on your calculator
To evaluate csc x, sec x & cot x, you will need to utilize the fact that
they are reciprocal functions
1
1
1
Remember:
csc x
sec x
cot x
sin x
cos x
tan x
Ex 2) Find the value (round to 4 dec. places)
a) sec 146°
(degree mode)
1
sec146
1.2062
cos146
b) cot 39° 52ʹ 15ʺ
(degree mode)
1
cot 395215
1.1972
tan 395215
OR
cot 39.8708
1
tan 39.8708
1.1972
We can also solve for an angle (in degrees or radians) if we know the
ratio. Use the inverse trig functions (sin–1θ, cos–1θ, tan–1θ)
*Often these problems can have more than 1 answer – you need to
think and draw a sketch!!
Ex 3) Find the values of θ where 0° ≤ θ < 360° (round to
(degree mode!!)
nearest tenth)
a) sin θ = 0.7193
θ
θ = sin–1(0.7193)
θ = 46.0° AND…sinθ is (+) in QI
θ
& QII
180 – 46 = 134.0°
θ = 46.0° and 134.0°
Ex 3) Find the values of θ where 0° ≤ θ < 360° (round to
(degree mode!!)
nearest tenth)
b) tan θ = –0.2309
θ = tan–1(–0.2309)
θ = –13.0°
tanθ is (–) in QIV & QII
13.0°
–13.0°
180 – 13 = 167.0°
360 – 13 = 347.0°
θ = 167.0° and 347.0°
Ex 4) Find the values of θ where 0 ≤ θ < 2π (round to nearest
(radian mode!!)
hundredth)
a) cos θ = –0.4611
θ = cos–1(–0.4611)
2.05
θ = 2.05
–2.05
cosθ is (–) in QII
& QIII
θ = 2.05 rad and 4.23 rad
2π – 2.05 = 4.23
Ex 4) Find the values of θ where 0 ≤ θ < 2π (round to nearest
hundredth)
(radian mode!!)
b) sec θ = 8.2986
1
8.2986
cos
1
cos
8.2986
1
1
cos
8.2986
1.45
1.45
–1.45
cosθ is (+) in QI
θ = 1.45 rad and 4.83 rad
& QIV
2π – 1.45 = 4.83
Homework
#307 Pg 163 #1–41 odd, 44
Slide 3
3.7 Evaluating Trig Functions
To properly evaluate trig ratios on our calculator, we need to
make sure we are in the right MODE – Degrees or Radians
If it has a degree symbol put in Degree Mode
If no symbol at all put in Radian Mode
Ex 1) Find the value (round to 4 dec. places)
a) cos 275°
(degree mode)
cos 275° = 0.0872
b) sin (–1.4π) (radian mode) sin (–1.4π) = 0.9511
c) tan 2
(radian mode) tan 2 = –2.1850
To evaluate ratios when given Deg-Min-Sec, either convert to just
degrees or use the °, ʹ, ʺ buttons on your calculator
To evaluate csc x, sec x & cot x, you will need to utilize the fact that
they are reciprocal functions
1
1
1
Remember:
csc x
sec x
cot x
sin x
cos x
tan x
Ex 2) Find the value (round to 4 dec. places)
a) sec 146°
(degree mode)
1
sec146
1.2062
cos146
b) cot 39° 52ʹ 15ʺ
(degree mode)
1
cot 395215
1.1972
tan 395215
OR
cot 39.8708
1
tan 39.8708
1.1972
We can also solve for an angle (in degrees or radians) if we know the
ratio. Use the inverse trig functions (sin–1θ, cos–1θ, tan–1θ)
*Often these problems can have more than 1 answer – you need to
think and draw a sketch!!
Ex 3) Find the values of θ where 0° ≤ θ < 360° (round to
(degree mode!!)
nearest tenth)
a) sin θ = 0.7193
θ
θ = sin–1(0.7193)
θ = 46.0° AND…sinθ is (+) in QI
θ
& QII
180 – 46 = 134.0°
θ = 46.0° and 134.0°
Ex 3) Find the values of θ where 0° ≤ θ < 360° (round to
(degree mode!!)
nearest tenth)
b) tan θ = –0.2309
θ = tan–1(–0.2309)
θ = –13.0°
tanθ is (–) in QIV & QII
13.0°
–13.0°
180 – 13 = 167.0°
360 – 13 = 347.0°
θ = 167.0° and 347.0°
Ex 4) Find the values of θ where 0 ≤ θ < 2π (round to nearest
(radian mode!!)
hundredth)
a) cos θ = –0.4611
θ = cos–1(–0.4611)
2.05
θ = 2.05
–2.05
cosθ is (–) in QII
& QIII
θ = 2.05 rad and 4.23 rad
2π – 2.05 = 4.23
Ex 4) Find the values of θ where 0 ≤ θ < 2π (round to nearest
hundredth)
(radian mode!!)
b) sec θ = 8.2986
1
8.2986
cos
1
cos
8.2986
1
1
cos
8.2986
1.45
1.45
–1.45
cosθ is (+) in QI
θ = 1.45 rad and 4.83 rad
& QIV
2π – 1.45 = 4.83
Homework
#307 Pg 163 #1–41 odd, 44
Slide 4
3.7 Evaluating Trig Functions
To properly evaluate trig ratios on our calculator, we need to
make sure we are in the right MODE – Degrees or Radians
If it has a degree symbol put in Degree Mode
If no symbol at all put in Radian Mode
Ex 1) Find the value (round to 4 dec. places)
a) cos 275°
(degree mode)
cos 275° = 0.0872
b) sin (–1.4π) (radian mode) sin (–1.4π) = 0.9511
c) tan 2
(radian mode) tan 2 = –2.1850
To evaluate ratios when given Deg-Min-Sec, either convert to just
degrees or use the °, ʹ, ʺ buttons on your calculator
To evaluate csc x, sec x & cot x, you will need to utilize the fact that
they are reciprocal functions
1
1
1
Remember:
csc x
sec x
cot x
sin x
cos x
tan x
Ex 2) Find the value (round to 4 dec. places)
a) sec 146°
(degree mode)
1
sec146
1.2062
cos146
b) cot 39° 52ʹ 15ʺ
(degree mode)
1
cot 395215
1.1972
tan 395215
OR
cot 39.8708
1
tan 39.8708
1.1972
We can also solve for an angle (in degrees or radians) if we know the
ratio. Use the inverse trig functions (sin–1θ, cos–1θ, tan–1θ)
*Often these problems can have more than 1 answer – you need to
think and draw a sketch!!
Ex 3) Find the values of θ where 0° ≤ θ < 360° (round to
(degree mode!!)
nearest tenth)
a) sin θ = 0.7193
θ
θ = sin–1(0.7193)
θ = 46.0° AND…sinθ is (+) in QI
θ
& QII
180 – 46 = 134.0°
θ = 46.0° and 134.0°
Ex 3) Find the values of θ where 0° ≤ θ < 360° (round to
(degree mode!!)
nearest tenth)
b) tan θ = –0.2309
θ = tan–1(–0.2309)
θ = –13.0°
tanθ is (–) in QIV & QII
13.0°
–13.0°
180 – 13 = 167.0°
360 – 13 = 347.0°
θ = 167.0° and 347.0°
Ex 4) Find the values of θ where 0 ≤ θ < 2π (round to nearest
(radian mode!!)
hundredth)
a) cos θ = –0.4611
θ = cos–1(–0.4611)
2.05
θ = 2.05
–2.05
cosθ is (–) in QII
& QIII
θ = 2.05 rad and 4.23 rad
2π – 2.05 = 4.23
Ex 4) Find the values of θ where 0 ≤ θ < 2π (round to nearest
hundredth)
(radian mode!!)
b) sec θ = 8.2986
1
8.2986
cos
1
cos
8.2986
1
1
cos
8.2986
1.45
1.45
–1.45
cosθ is (+) in QI
θ = 1.45 rad and 4.83 rad
& QIV
2π – 1.45 = 4.83
Homework
#307 Pg 163 #1–41 odd, 44
Slide 5
3.7 Evaluating Trig Functions
To properly evaluate trig ratios on our calculator, we need to
make sure we are in the right MODE – Degrees or Radians
If it has a degree symbol put in Degree Mode
If no symbol at all put in Radian Mode
Ex 1) Find the value (round to 4 dec. places)
a) cos 275°
(degree mode)
cos 275° = 0.0872
b) sin (–1.4π) (radian mode) sin (–1.4π) = 0.9511
c) tan 2
(radian mode) tan 2 = –2.1850
To evaluate ratios when given Deg-Min-Sec, either convert to just
degrees or use the °, ʹ, ʺ buttons on your calculator
To evaluate csc x, sec x & cot x, you will need to utilize the fact that
they are reciprocal functions
1
1
1
Remember:
csc x
sec x
cot x
sin x
cos x
tan x
Ex 2) Find the value (round to 4 dec. places)
a) sec 146°
(degree mode)
1
sec146
1.2062
cos146
b) cot 39° 52ʹ 15ʺ
(degree mode)
1
cot 395215
1.1972
tan 395215
OR
cot 39.8708
1
tan 39.8708
1.1972
We can also solve for an angle (in degrees or radians) if we know the
ratio. Use the inverse trig functions (sin–1θ, cos–1θ, tan–1θ)
*Often these problems can have more than 1 answer – you need to
think and draw a sketch!!
Ex 3) Find the values of θ where 0° ≤ θ < 360° (round to
(degree mode!!)
nearest tenth)
a) sin θ = 0.7193
θ
θ = sin–1(0.7193)
θ = 46.0° AND…sinθ is (+) in QI
θ
& QII
180 – 46 = 134.0°
θ = 46.0° and 134.0°
Ex 3) Find the values of θ where 0° ≤ θ < 360° (round to
(degree mode!!)
nearest tenth)
b) tan θ = –0.2309
θ = tan–1(–0.2309)
θ = –13.0°
tanθ is (–) in QIV & QII
13.0°
–13.0°
180 – 13 = 167.0°
360 – 13 = 347.0°
θ = 167.0° and 347.0°
Ex 4) Find the values of θ where 0 ≤ θ < 2π (round to nearest
(radian mode!!)
hundredth)
a) cos θ = –0.4611
θ = cos–1(–0.4611)
2.05
θ = 2.05
–2.05
cosθ is (–) in QII
& QIII
θ = 2.05 rad and 4.23 rad
2π – 2.05 = 4.23
Ex 4) Find the values of θ where 0 ≤ θ < 2π (round to nearest
hundredth)
(radian mode!!)
b) sec θ = 8.2986
1
8.2986
cos
1
cos
8.2986
1
1
cos
8.2986
1.45
1.45
–1.45
cosθ is (+) in QI
θ = 1.45 rad and 4.83 rad
& QIV
2π – 1.45 = 4.83
Homework
#307 Pg 163 #1–41 odd, 44
Slide 6
3.7 Evaluating Trig Functions
To properly evaluate trig ratios on our calculator, we need to
make sure we are in the right MODE – Degrees or Radians
If it has a degree symbol put in Degree Mode
If no symbol at all put in Radian Mode
Ex 1) Find the value (round to 4 dec. places)
a) cos 275°
(degree mode)
cos 275° = 0.0872
b) sin (–1.4π) (radian mode) sin (–1.4π) = 0.9511
c) tan 2
(radian mode) tan 2 = –2.1850
To evaluate ratios when given Deg-Min-Sec, either convert to just
degrees or use the °, ʹ, ʺ buttons on your calculator
To evaluate csc x, sec x & cot x, you will need to utilize the fact that
they are reciprocal functions
1
1
1
Remember:
csc x
sec x
cot x
sin x
cos x
tan x
Ex 2) Find the value (round to 4 dec. places)
a) sec 146°
(degree mode)
1
sec146
1.2062
cos146
b) cot 39° 52ʹ 15ʺ
(degree mode)
1
cot 395215
1.1972
tan 395215
OR
cot 39.8708
1
tan 39.8708
1.1972
We can also solve for an angle (in degrees or radians) if we know the
ratio. Use the inverse trig functions (sin–1θ, cos–1θ, tan–1θ)
*Often these problems can have more than 1 answer – you need to
think and draw a sketch!!
Ex 3) Find the values of θ where 0° ≤ θ < 360° (round to
(degree mode!!)
nearest tenth)
a) sin θ = 0.7193
θ
θ = sin–1(0.7193)
θ = 46.0° AND…sinθ is (+) in QI
θ
& QII
180 – 46 = 134.0°
θ = 46.0° and 134.0°
Ex 3) Find the values of θ where 0° ≤ θ < 360° (round to
(degree mode!!)
nearest tenth)
b) tan θ = –0.2309
θ = tan–1(–0.2309)
θ = –13.0°
tanθ is (–) in QIV & QII
13.0°
–13.0°
180 – 13 = 167.0°
360 – 13 = 347.0°
θ = 167.0° and 347.0°
Ex 4) Find the values of θ where 0 ≤ θ < 2π (round to nearest
(radian mode!!)
hundredth)
a) cos θ = –0.4611
θ = cos–1(–0.4611)
2.05
θ = 2.05
–2.05
cosθ is (–) in QII
& QIII
θ = 2.05 rad and 4.23 rad
2π – 2.05 = 4.23
Ex 4) Find the values of θ where 0 ≤ θ < 2π (round to nearest
hundredth)
(radian mode!!)
b) sec θ = 8.2986
1
8.2986
cos
1
cos
8.2986
1
1
cos
8.2986
1.45
1.45
–1.45
cosθ is (+) in QI
θ = 1.45 rad and 4.83 rad
& QIV
2π – 1.45 = 4.83
Homework
#307 Pg 163 #1–41 odd, 44
Slide 7
3.7 Evaluating Trig Functions
To properly evaluate trig ratios on our calculator, we need to
make sure we are in the right MODE – Degrees or Radians
If it has a degree symbol put in Degree Mode
If no symbol at all put in Radian Mode
Ex 1) Find the value (round to 4 dec. places)
a) cos 275°
(degree mode)
cos 275° = 0.0872
b) sin (–1.4π) (radian mode) sin (–1.4π) = 0.9511
c) tan 2
(radian mode) tan 2 = –2.1850
To evaluate ratios when given Deg-Min-Sec, either convert to just
degrees or use the °, ʹ, ʺ buttons on your calculator
To evaluate csc x, sec x & cot x, you will need to utilize the fact that
they are reciprocal functions
1
1
1
Remember:
csc x
sec x
cot x
sin x
cos x
tan x
Ex 2) Find the value (round to 4 dec. places)
a) sec 146°
(degree mode)
1
sec146
1.2062
cos146
b) cot 39° 52ʹ 15ʺ
(degree mode)
1
cot 395215
1.1972
tan 395215
OR
cot 39.8708
1
tan 39.8708
1.1972
We can also solve for an angle (in degrees or radians) if we know the
ratio. Use the inverse trig functions (sin–1θ, cos–1θ, tan–1θ)
*Often these problems can have more than 1 answer – you need to
think and draw a sketch!!
Ex 3) Find the values of θ where 0° ≤ θ < 360° (round to
(degree mode!!)
nearest tenth)
a) sin θ = 0.7193
θ
θ = sin–1(0.7193)
θ = 46.0° AND…sinθ is (+) in QI
θ
& QII
180 – 46 = 134.0°
θ = 46.0° and 134.0°
Ex 3) Find the values of θ where 0° ≤ θ < 360° (round to
(degree mode!!)
nearest tenth)
b) tan θ = –0.2309
θ = tan–1(–0.2309)
θ = –13.0°
tanθ is (–) in QIV & QII
13.0°
–13.0°
180 – 13 = 167.0°
360 – 13 = 347.0°
θ = 167.0° and 347.0°
Ex 4) Find the values of θ where 0 ≤ θ < 2π (round to nearest
(radian mode!!)
hundredth)
a) cos θ = –0.4611
θ = cos–1(–0.4611)
2.05
θ = 2.05
–2.05
cosθ is (–) in QII
& QIII
θ = 2.05 rad and 4.23 rad
2π – 2.05 = 4.23
Ex 4) Find the values of θ where 0 ≤ θ < 2π (round to nearest
hundredth)
(radian mode!!)
b) sec θ = 8.2986
1
8.2986
cos
1
cos
8.2986
1
1
cos
8.2986
1.45
1.45
–1.45
cosθ is (+) in QI
θ = 1.45 rad and 4.83 rad
& QIV
2π – 1.45 = 4.83
Homework
#307 Pg 163 #1–41 odd, 44
Slide 8
3.7 Evaluating Trig Functions
To properly evaluate trig ratios on our calculator, we need to
make sure we are in the right MODE – Degrees or Radians
If it has a degree symbol put in Degree Mode
If no symbol at all put in Radian Mode
Ex 1) Find the value (round to 4 dec. places)
a) cos 275°
(degree mode)
cos 275° = 0.0872
b) sin (–1.4π) (radian mode) sin (–1.4π) = 0.9511
c) tan 2
(radian mode) tan 2 = –2.1850
To evaluate ratios when given Deg-Min-Sec, either convert to just
degrees or use the °, ʹ, ʺ buttons on your calculator
To evaluate csc x, sec x & cot x, you will need to utilize the fact that
they are reciprocal functions
1
1
1
Remember:
csc x
sec x
cot x
sin x
cos x
tan x
Ex 2) Find the value (round to 4 dec. places)
a) sec 146°
(degree mode)
1
sec146
1.2062
cos146
b) cot 39° 52ʹ 15ʺ
(degree mode)
1
cot 395215
1.1972
tan 395215
OR
cot 39.8708
1
tan 39.8708
1.1972
We can also solve for an angle (in degrees or radians) if we know the
ratio. Use the inverse trig functions (sin–1θ, cos–1θ, tan–1θ)
*Often these problems can have more than 1 answer – you need to
think and draw a sketch!!
Ex 3) Find the values of θ where 0° ≤ θ < 360° (round to
(degree mode!!)
nearest tenth)
a) sin θ = 0.7193
θ
θ = sin–1(0.7193)
θ = 46.0° AND…sinθ is (+) in QI
θ
& QII
180 – 46 = 134.0°
θ = 46.0° and 134.0°
Ex 3) Find the values of θ where 0° ≤ θ < 360° (round to
(degree mode!!)
nearest tenth)
b) tan θ = –0.2309
θ = tan–1(–0.2309)
θ = –13.0°
tanθ is (–) in QIV & QII
13.0°
–13.0°
180 – 13 = 167.0°
360 – 13 = 347.0°
θ = 167.0° and 347.0°
Ex 4) Find the values of θ where 0 ≤ θ < 2π (round to nearest
(radian mode!!)
hundredth)
a) cos θ = –0.4611
θ = cos–1(–0.4611)
2.05
θ = 2.05
–2.05
cosθ is (–) in QII
& QIII
θ = 2.05 rad and 4.23 rad
2π – 2.05 = 4.23
Ex 4) Find the values of θ where 0 ≤ θ < 2π (round to nearest
hundredth)
(radian mode!!)
b) sec θ = 8.2986
1
8.2986
cos
1
cos
8.2986
1
1
cos
8.2986
1.45
1.45
–1.45
cosθ is (+) in QI
θ = 1.45 rad and 4.83 rad
& QIV
2π – 1.45 = 4.83
Homework
#307 Pg 163 #1–41 odd, 44
3.7 Evaluating Trig Functions
To properly evaluate trig ratios on our calculator, we need to
make sure we are in the right MODE – Degrees or Radians
If it has a degree symbol put in Degree Mode
If no symbol at all put in Radian Mode
Ex 1) Find the value (round to 4 dec. places)
a) cos 275°
(degree mode)
cos 275° = 0.0872
b) sin (–1.4π) (radian mode) sin (–1.4π) = 0.9511
c) tan 2
(radian mode) tan 2 = –2.1850
To evaluate ratios when given Deg-Min-Sec, either convert to just
degrees or use the °, ʹ, ʺ buttons on your calculator
To evaluate csc x, sec x & cot x, you will need to utilize the fact that
they are reciprocal functions
1
1
1
Remember:
csc x
sec x
cot x
sin x
cos x
tan x
Ex 2) Find the value (round to 4 dec. places)
a) sec 146°
(degree mode)
1
sec146
1.2062
cos146
b) cot 39° 52ʹ 15ʺ
(degree mode)
1
cot 395215
1.1972
tan 395215
OR
cot 39.8708
1
tan 39.8708
1.1972
We can also solve for an angle (in degrees or radians) if we know the
ratio. Use the inverse trig functions (sin–1θ, cos–1θ, tan–1θ)
*Often these problems can have more than 1 answer – you need to
think and draw a sketch!!
Ex 3) Find the values of θ where 0° ≤ θ < 360° (round to
(degree mode!!)
nearest tenth)
a) sin θ = 0.7193
θ
θ = sin–1(0.7193)
θ = 46.0° AND…sinθ is (+) in QI
θ
& QII
180 – 46 = 134.0°
θ = 46.0° and 134.0°
Ex 3) Find the values of θ where 0° ≤ θ < 360° (round to
(degree mode!!)
nearest tenth)
b) tan θ = –0.2309
θ = tan–1(–0.2309)
θ = –13.0°
tanθ is (–) in QIV & QII
13.0°
–13.0°
180 – 13 = 167.0°
360 – 13 = 347.0°
θ = 167.0° and 347.0°
Ex 4) Find the values of θ where 0 ≤ θ < 2π (round to nearest
(radian mode!!)
hundredth)
a) cos θ = –0.4611
θ = cos–1(–0.4611)
2.05
θ = 2.05
–2.05
cosθ is (–) in QII
& QIII
θ = 2.05 rad and 4.23 rad
2π – 2.05 = 4.23
Ex 4) Find the values of θ where 0 ≤ θ < 2π (round to nearest
hundredth)
(radian mode!!)
b) sec θ = 8.2986
1
8.2986
cos
1
cos
8.2986
1
1
cos
8.2986
1.45
1.45
–1.45
cosθ is (+) in QI
θ = 1.45 rad and 4.83 rad
& QIV
2π – 1.45 = 4.83
Homework
#307 Pg 163 #1–41 odd, 44
Slide 2
3.7 Evaluating Trig Functions
To properly evaluate trig ratios on our calculator, we need to
make sure we are in the right MODE – Degrees or Radians
If it has a degree symbol put in Degree Mode
If no symbol at all put in Radian Mode
Ex 1) Find the value (round to 4 dec. places)
a) cos 275°
(degree mode)
cos 275° = 0.0872
b) sin (–1.4π) (radian mode) sin (–1.4π) = 0.9511
c) tan 2
(radian mode) tan 2 = –2.1850
To evaluate ratios when given Deg-Min-Sec, either convert to just
degrees or use the °, ʹ, ʺ buttons on your calculator
To evaluate csc x, sec x & cot x, you will need to utilize the fact that
they are reciprocal functions
1
1
1
Remember:
csc x
sec x
cot x
sin x
cos x
tan x
Ex 2) Find the value (round to 4 dec. places)
a) sec 146°
(degree mode)
1
sec146
1.2062
cos146
b) cot 39° 52ʹ 15ʺ
(degree mode)
1
cot 395215
1.1972
tan 395215
OR
cot 39.8708
1
tan 39.8708
1.1972
We can also solve for an angle (in degrees or radians) if we know the
ratio. Use the inverse trig functions (sin–1θ, cos–1θ, tan–1θ)
*Often these problems can have more than 1 answer – you need to
think and draw a sketch!!
Ex 3) Find the values of θ where 0° ≤ θ < 360° (round to
(degree mode!!)
nearest tenth)
a) sin θ = 0.7193
θ
θ = sin–1(0.7193)
θ = 46.0° AND…sinθ is (+) in QI
θ
& QII
180 – 46 = 134.0°
θ = 46.0° and 134.0°
Ex 3) Find the values of θ where 0° ≤ θ < 360° (round to
(degree mode!!)
nearest tenth)
b) tan θ = –0.2309
θ = tan–1(–0.2309)
θ = –13.0°
tanθ is (–) in QIV & QII
13.0°
–13.0°
180 – 13 = 167.0°
360 – 13 = 347.0°
θ = 167.0° and 347.0°
Ex 4) Find the values of θ where 0 ≤ θ < 2π (round to nearest
(radian mode!!)
hundredth)
a) cos θ = –0.4611
θ = cos–1(–0.4611)
2.05
θ = 2.05
–2.05
cosθ is (–) in QII
& QIII
θ = 2.05 rad and 4.23 rad
2π – 2.05 = 4.23
Ex 4) Find the values of θ where 0 ≤ θ < 2π (round to nearest
hundredth)
(radian mode!!)
b) sec θ = 8.2986
1
8.2986
cos
1
cos
8.2986
1
1
cos
8.2986
1.45
1.45
–1.45
cosθ is (+) in QI
θ = 1.45 rad and 4.83 rad
& QIV
2π – 1.45 = 4.83
Homework
#307 Pg 163 #1–41 odd, 44
Slide 3
3.7 Evaluating Trig Functions
To properly evaluate trig ratios on our calculator, we need to
make sure we are in the right MODE – Degrees or Radians
If it has a degree symbol put in Degree Mode
If no symbol at all put in Radian Mode
Ex 1) Find the value (round to 4 dec. places)
a) cos 275°
(degree mode)
cos 275° = 0.0872
b) sin (–1.4π) (radian mode) sin (–1.4π) = 0.9511
c) tan 2
(radian mode) tan 2 = –2.1850
To evaluate ratios when given Deg-Min-Sec, either convert to just
degrees or use the °, ʹ, ʺ buttons on your calculator
To evaluate csc x, sec x & cot x, you will need to utilize the fact that
they are reciprocal functions
1
1
1
Remember:
csc x
sec x
cot x
sin x
cos x
tan x
Ex 2) Find the value (round to 4 dec. places)
a) sec 146°
(degree mode)
1
sec146
1.2062
cos146
b) cot 39° 52ʹ 15ʺ
(degree mode)
1
cot 395215
1.1972
tan 395215
OR
cot 39.8708
1
tan 39.8708
1.1972
We can also solve for an angle (in degrees or radians) if we know the
ratio. Use the inverse trig functions (sin–1θ, cos–1θ, tan–1θ)
*Often these problems can have more than 1 answer – you need to
think and draw a sketch!!
Ex 3) Find the values of θ where 0° ≤ θ < 360° (round to
(degree mode!!)
nearest tenth)
a) sin θ = 0.7193
θ
θ = sin–1(0.7193)
θ = 46.0° AND…sinθ is (+) in QI
θ
& QII
180 – 46 = 134.0°
θ = 46.0° and 134.0°
Ex 3) Find the values of θ where 0° ≤ θ < 360° (round to
(degree mode!!)
nearest tenth)
b) tan θ = –0.2309
θ = tan–1(–0.2309)
θ = –13.0°
tanθ is (–) in QIV & QII
13.0°
–13.0°
180 – 13 = 167.0°
360 – 13 = 347.0°
θ = 167.0° and 347.0°
Ex 4) Find the values of θ where 0 ≤ θ < 2π (round to nearest
(radian mode!!)
hundredth)
a) cos θ = –0.4611
θ = cos–1(–0.4611)
2.05
θ = 2.05
–2.05
cosθ is (–) in QII
& QIII
θ = 2.05 rad and 4.23 rad
2π – 2.05 = 4.23
Ex 4) Find the values of θ where 0 ≤ θ < 2π (round to nearest
hundredth)
(radian mode!!)
b) sec θ = 8.2986
1
8.2986
cos
1
cos
8.2986
1
1
cos
8.2986
1.45
1.45
–1.45
cosθ is (+) in QI
θ = 1.45 rad and 4.83 rad
& QIV
2π – 1.45 = 4.83
Homework
#307 Pg 163 #1–41 odd, 44
Slide 4
3.7 Evaluating Trig Functions
To properly evaluate trig ratios on our calculator, we need to
make sure we are in the right MODE – Degrees or Radians
If it has a degree symbol put in Degree Mode
If no symbol at all put in Radian Mode
Ex 1) Find the value (round to 4 dec. places)
a) cos 275°
(degree mode)
cos 275° = 0.0872
b) sin (–1.4π) (radian mode) sin (–1.4π) = 0.9511
c) tan 2
(radian mode) tan 2 = –2.1850
To evaluate ratios when given Deg-Min-Sec, either convert to just
degrees or use the °, ʹ, ʺ buttons on your calculator
To evaluate csc x, sec x & cot x, you will need to utilize the fact that
they are reciprocal functions
1
1
1
Remember:
csc x
sec x
cot x
sin x
cos x
tan x
Ex 2) Find the value (round to 4 dec. places)
a) sec 146°
(degree mode)
1
sec146
1.2062
cos146
b) cot 39° 52ʹ 15ʺ
(degree mode)
1
cot 395215
1.1972
tan 395215
OR
cot 39.8708
1
tan 39.8708
1.1972
We can also solve for an angle (in degrees or radians) if we know the
ratio. Use the inverse trig functions (sin–1θ, cos–1θ, tan–1θ)
*Often these problems can have more than 1 answer – you need to
think and draw a sketch!!
Ex 3) Find the values of θ where 0° ≤ θ < 360° (round to
(degree mode!!)
nearest tenth)
a) sin θ = 0.7193
θ
θ = sin–1(0.7193)
θ = 46.0° AND…sinθ is (+) in QI
θ
& QII
180 – 46 = 134.0°
θ = 46.0° and 134.0°
Ex 3) Find the values of θ where 0° ≤ θ < 360° (round to
(degree mode!!)
nearest tenth)
b) tan θ = –0.2309
θ = tan–1(–0.2309)
θ = –13.0°
tanθ is (–) in QIV & QII
13.0°
–13.0°
180 – 13 = 167.0°
360 – 13 = 347.0°
θ = 167.0° and 347.0°
Ex 4) Find the values of θ where 0 ≤ θ < 2π (round to nearest
(radian mode!!)
hundredth)
a) cos θ = –0.4611
θ = cos–1(–0.4611)
2.05
θ = 2.05
–2.05
cosθ is (–) in QII
& QIII
θ = 2.05 rad and 4.23 rad
2π – 2.05 = 4.23
Ex 4) Find the values of θ where 0 ≤ θ < 2π (round to nearest
hundredth)
(radian mode!!)
b) sec θ = 8.2986
1
8.2986
cos
1
cos
8.2986
1
1
cos
8.2986
1.45
1.45
–1.45
cosθ is (+) in QI
θ = 1.45 rad and 4.83 rad
& QIV
2π – 1.45 = 4.83
Homework
#307 Pg 163 #1–41 odd, 44
Slide 5
3.7 Evaluating Trig Functions
To properly evaluate trig ratios on our calculator, we need to
make sure we are in the right MODE – Degrees or Radians
If it has a degree symbol put in Degree Mode
If no symbol at all put in Radian Mode
Ex 1) Find the value (round to 4 dec. places)
a) cos 275°
(degree mode)
cos 275° = 0.0872
b) sin (–1.4π) (radian mode) sin (–1.4π) = 0.9511
c) tan 2
(radian mode) tan 2 = –2.1850
To evaluate ratios when given Deg-Min-Sec, either convert to just
degrees or use the °, ʹ, ʺ buttons on your calculator
To evaluate csc x, sec x & cot x, you will need to utilize the fact that
they are reciprocal functions
1
1
1
Remember:
csc x
sec x
cot x
sin x
cos x
tan x
Ex 2) Find the value (round to 4 dec. places)
a) sec 146°
(degree mode)
1
sec146
1.2062
cos146
b) cot 39° 52ʹ 15ʺ
(degree mode)
1
cot 395215
1.1972
tan 395215
OR
cot 39.8708
1
tan 39.8708
1.1972
We can also solve for an angle (in degrees or radians) if we know the
ratio. Use the inverse trig functions (sin–1θ, cos–1θ, tan–1θ)
*Often these problems can have more than 1 answer – you need to
think and draw a sketch!!
Ex 3) Find the values of θ where 0° ≤ θ < 360° (round to
(degree mode!!)
nearest tenth)
a) sin θ = 0.7193
θ
θ = sin–1(0.7193)
θ = 46.0° AND…sinθ is (+) in QI
θ
& QII
180 – 46 = 134.0°
θ = 46.0° and 134.0°
Ex 3) Find the values of θ where 0° ≤ θ < 360° (round to
(degree mode!!)
nearest tenth)
b) tan θ = –0.2309
θ = tan–1(–0.2309)
θ = –13.0°
tanθ is (–) in QIV & QII
13.0°
–13.0°
180 – 13 = 167.0°
360 – 13 = 347.0°
θ = 167.0° and 347.0°
Ex 4) Find the values of θ where 0 ≤ θ < 2π (round to nearest
(radian mode!!)
hundredth)
a) cos θ = –0.4611
θ = cos–1(–0.4611)
2.05
θ = 2.05
–2.05
cosθ is (–) in QII
& QIII
θ = 2.05 rad and 4.23 rad
2π – 2.05 = 4.23
Ex 4) Find the values of θ where 0 ≤ θ < 2π (round to nearest
hundredth)
(radian mode!!)
b) sec θ = 8.2986
1
8.2986
cos
1
cos
8.2986
1
1
cos
8.2986
1.45
1.45
–1.45
cosθ is (+) in QI
θ = 1.45 rad and 4.83 rad
& QIV
2π – 1.45 = 4.83
Homework
#307 Pg 163 #1–41 odd, 44
Slide 6
3.7 Evaluating Trig Functions
To properly evaluate trig ratios on our calculator, we need to
make sure we are in the right MODE – Degrees or Radians
If it has a degree symbol put in Degree Mode
If no symbol at all put in Radian Mode
Ex 1) Find the value (round to 4 dec. places)
a) cos 275°
(degree mode)
cos 275° = 0.0872
b) sin (–1.4π) (radian mode) sin (–1.4π) = 0.9511
c) tan 2
(radian mode) tan 2 = –2.1850
To evaluate ratios when given Deg-Min-Sec, either convert to just
degrees or use the °, ʹ, ʺ buttons on your calculator
To evaluate csc x, sec x & cot x, you will need to utilize the fact that
they are reciprocal functions
1
1
1
Remember:
csc x
sec x
cot x
sin x
cos x
tan x
Ex 2) Find the value (round to 4 dec. places)
a) sec 146°
(degree mode)
1
sec146
1.2062
cos146
b) cot 39° 52ʹ 15ʺ
(degree mode)
1
cot 395215
1.1972
tan 395215
OR
cot 39.8708
1
tan 39.8708
1.1972
We can also solve for an angle (in degrees or radians) if we know the
ratio. Use the inverse trig functions (sin–1θ, cos–1θ, tan–1θ)
*Often these problems can have more than 1 answer – you need to
think and draw a sketch!!
Ex 3) Find the values of θ where 0° ≤ θ < 360° (round to
(degree mode!!)
nearest tenth)
a) sin θ = 0.7193
θ
θ = sin–1(0.7193)
θ = 46.0° AND…sinθ is (+) in QI
θ
& QII
180 – 46 = 134.0°
θ = 46.0° and 134.0°
Ex 3) Find the values of θ where 0° ≤ θ < 360° (round to
(degree mode!!)
nearest tenth)
b) tan θ = –0.2309
θ = tan–1(–0.2309)
θ = –13.0°
tanθ is (–) in QIV & QII
13.0°
–13.0°
180 – 13 = 167.0°
360 – 13 = 347.0°
θ = 167.0° and 347.0°
Ex 4) Find the values of θ where 0 ≤ θ < 2π (round to nearest
(radian mode!!)
hundredth)
a) cos θ = –0.4611
θ = cos–1(–0.4611)
2.05
θ = 2.05
–2.05
cosθ is (–) in QII
& QIII
θ = 2.05 rad and 4.23 rad
2π – 2.05 = 4.23
Ex 4) Find the values of θ where 0 ≤ θ < 2π (round to nearest
hundredth)
(radian mode!!)
b) sec θ = 8.2986
1
8.2986
cos
1
cos
8.2986
1
1
cos
8.2986
1.45
1.45
–1.45
cosθ is (+) in QI
θ = 1.45 rad and 4.83 rad
& QIV
2π – 1.45 = 4.83
Homework
#307 Pg 163 #1–41 odd, 44
Slide 7
3.7 Evaluating Trig Functions
To properly evaluate trig ratios on our calculator, we need to
make sure we are in the right MODE – Degrees or Radians
If it has a degree symbol put in Degree Mode
If no symbol at all put in Radian Mode
Ex 1) Find the value (round to 4 dec. places)
a) cos 275°
(degree mode)
cos 275° = 0.0872
b) sin (–1.4π) (radian mode) sin (–1.4π) = 0.9511
c) tan 2
(radian mode) tan 2 = –2.1850
To evaluate ratios when given Deg-Min-Sec, either convert to just
degrees or use the °, ʹ, ʺ buttons on your calculator
To evaluate csc x, sec x & cot x, you will need to utilize the fact that
they are reciprocal functions
1
1
1
Remember:
csc x
sec x
cot x
sin x
cos x
tan x
Ex 2) Find the value (round to 4 dec. places)
a) sec 146°
(degree mode)
1
sec146
1.2062
cos146
b) cot 39° 52ʹ 15ʺ
(degree mode)
1
cot 395215
1.1972
tan 395215
OR
cot 39.8708
1
tan 39.8708
1.1972
We can also solve for an angle (in degrees or radians) if we know the
ratio. Use the inverse trig functions (sin–1θ, cos–1θ, tan–1θ)
*Often these problems can have more than 1 answer – you need to
think and draw a sketch!!
Ex 3) Find the values of θ where 0° ≤ θ < 360° (round to
(degree mode!!)
nearest tenth)
a) sin θ = 0.7193
θ
θ = sin–1(0.7193)
θ = 46.0° AND…sinθ is (+) in QI
θ
& QII
180 – 46 = 134.0°
θ = 46.0° and 134.0°
Ex 3) Find the values of θ where 0° ≤ θ < 360° (round to
(degree mode!!)
nearest tenth)
b) tan θ = –0.2309
θ = tan–1(–0.2309)
θ = –13.0°
tanθ is (–) in QIV & QII
13.0°
–13.0°
180 – 13 = 167.0°
360 – 13 = 347.0°
θ = 167.0° and 347.0°
Ex 4) Find the values of θ where 0 ≤ θ < 2π (round to nearest
(radian mode!!)
hundredth)
a) cos θ = –0.4611
θ = cos–1(–0.4611)
2.05
θ = 2.05
–2.05
cosθ is (–) in QII
& QIII
θ = 2.05 rad and 4.23 rad
2π – 2.05 = 4.23
Ex 4) Find the values of θ where 0 ≤ θ < 2π (round to nearest
hundredth)
(radian mode!!)
b) sec θ = 8.2986
1
8.2986
cos
1
cos
8.2986
1
1
cos
8.2986
1.45
1.45
–1.45
cosθ is (+) in QI
θ = 1.45 rad and 4.83 rad
& QIV
2π – 1.45 = 4.83
Homework
#307 Pg 163 #1–41 odd, 44
Slide 8
3.7 Evaluating Trig Functions
To properly evaluate trig ratios on our calculator, we need to
make sure we are in the right MODE – Degrees or Radians
If it has a degree symbol put in Degree Mode
If no symbol at all put in Radian Mode
Ex 1) Find the value (round to 4 dec. places)
a) cos 275°
(degree mode)
cos 275° = 0.0872
b) sin (–1.4π) (radian mode) sin (–1.4π) = 0.9511
c) tan 2
(radian mode) tan 2 = –2.1850
To evaluate ratios when given Deg-Min-Sec, either convert to just
degrees or use the °, ʹ, ʺ buttons on your calculator
To evaluate csc x, sec x & cot x, you will need to utilize the fact that
they are reciprocal functions
1
1
1
Remember:
csc x
sec x
cot x
sin x
cos x
tan x
Ex 2) Find the value (round to 4 dec. places)
a) sec 146°
(degree mode)
1
sec146
1.2062
cos146
b) cot 39° 52ʹ 15ʺ
(degree mode)
1
cot 395215
1.1972
tan 395215
OR
cot 39.8708
1
tan 39.8708
1.1972
We can also solve for an angle (in degrees or radians) if we know the
ratio. Use the inverse trig functions (sin–1θ, cos–1θ, tan–1θ)
*Often these problems can have more than 1 answer – you need to
think and draw a sketch!!
Ex 3) Find the values of θ where 0° ≤ θ < 360° (round to
(degree mode!!)
nearest tenth)
a) sin θ = 0.7193
θ
θ = sin–1(0.7193)
θ = 46.0° AND…sinθ is (+) in QI
θ
& QII
180 – 46 = 134.0°
θ = 46.0° and 134.0°
Ex 3) Find the values of θ where 0° ≤ θ < 360° (round to
(degree mode!!)
nearest tenth)
b) tan θ = –0.2309
θ = tan–1(–0.2309)
θ = –13.0°
tanθ is (–) in QIV & QII
13.0°
–13.0°
180 – 13 = 167.0°
360 – 13 = 347.0°
θ = 167.0° and 347.0°
Ex 4) Find the values of θ where 0 ≤ θ < 2π (round to nearest
(radian mode!!)
hundredth)
a) cos θ = –0.4611
θ = cos–1(–0.4611)
2.05
θ = 2.05
–2.05
cosθ is (–) in QII
& QIII
θ = 2.05 rad and 4.23 rad
2π – 2.05 = 4.23
Ex 4) Find the values of θ where 0 ≤ θ < 2π (round to nearest
hundredth)
(radian mode!!)
b) sec θ = 8.2986
1
8.2986
cos
1
cos
8.2986
1
1
cos
8.2986
1.45
1.45
–1.45
cosθ is (+) in QI
θ = 1.45 rad and 4.83 rad
& QIV
2π – 1.45 = 4.83
Homework
#307 Pg 163 #1–41 odd, 44