Transcript Solve the Following Triangles

Trigonometry Quizzes
Quiz #1
Quiz #8
Quiz #15
Quiz #2
Quiz #9
Quiz #16
Quiz #3
Quiz #10
Quiz #17
Quiz #4
Quiz #11
Quiz #18
Quiz #5
Quiz #12
Quiz #19
Quiz #6
Quiz #13
Quiz #20
Quiz #7
Quiz #14
Quiz #21
Menu
Definitions of Trigonometric
Values of Acute Angles
of a Right Triangle
• For the triangle at the right …
sin
cos
tan
cot
sec
csc






=
=
=
=
=
=
__________
__________
__________
__________
__________
__________
c
a

b
Menu
Definitions of Trigonometric
Values of Acute Angles
of a Right Triangle
• For the triangle at the right …
sin
cos
tan
cot
sec
csc






=
=
=
=
=
=
a
__________
c
b
__________
c
a
__________
b
b
__________
a
c
__________
b
c
__________
a
c
a

b
Menu
Definitions of Trigonometric
Values of Acute Angles
of a Right Triangle
• For the triangle at the right …
sin
cos
tan
cot
sec
csc






=
=
=
=
=
=
__________
__________
__________
__________
__________
__________
26
24

10
Simplify your answers by reducing any fractions!
Menu
Definitions of Trigonometric
Values of Acute Angles
of a Right Triangle
• For the triangle at the right …
sin
cos
tan
cot
sec
csc






=
=
=
=
=
=
12
__________
13
5
__________
13
12
__________
5
5
__________
12
13
__________
5
13
__________
12
26
24

10
Simplify your answers by reducing any fractions!
Menu
Trigonometric Values of the Acute
Angles of a Right Triangle.
Given that cot  = 1.5,
determine the following:
sin  = ______
c
a
cos  = ______
tan  = ______
sec  = ______

b
csc  = ______
Hint:
Let 1.5 = 3/2 and determine the values of a, b, and c in the diagram.
Menu
Trigonometric Values of the Acute
Angles of a Right Triangle.
Given that cot  = 1.5,
determine the following:
2
 2 13
3
 3 13
13
sin  = ______
13  c
a 2
13
cos  = ______
13
13
2
3
tan  = ______
13
sec  = ______3

13
b 3
csc  = ______2
Hint:
Let 1.5 = 3/2 and determine the values of a, b, and c in the diagram.
Menu
Trigonometric Values of the Acute
Angles of a Right Triangle.
a=6
sec  = 5
b=8
--------------------
c = 10
sin  = ______
--------------------
c
sin  = ______
cos  = ______
tan  = ______
a
cos  = ______
tan  = ______
cot  = ______

csc  = ______
b
Simplify your answers by reducing any fractions!
Menu
Trigonometric Values of the Acute
Angles of a Right Triangle.
a=6
sec  = 5
b=8
-------------------2 6
24
5
5
sin  = ______
c = 10
1
--------------------
c
3
5
sin  = ______
5
cos  = ______
4
tan  = ______
24  2 6
tan  = ______
1
4
3
a
5
cos  = ______
 6
12
24
cot  = ______

5
5 6
12
24
csc  = ______
b
Simplify your answers by reducing any fractions!
Menu
Trigonometric Values of Special Angles
Complete the following table. Answers must be exact.

sin 
cos 
tan 
0º
30º
45º
60º
90º
Menu
Trigonometric Values of Special Angles
Complete the following table. Answers must be exact.

sin 
cos 
0º
0
1
0
30º
1
3
3
45º
2
60º
3
90º
1
2
2
2
1
2
2
2
2
0
tan 
3
1
3
DNE
Menu
Solve the Following Triangles
(Use a calculator and round answers to 1 decimal place.)
B
A = _________
A = 52°
B = _________
B = _________
C = 90°
C = 90°
c
a
a = _________
a = 17
b=7
b = _________
c = 10
c = _________
A
b
C
Menu
Solve the Following Triangles
(Use a calculator and round answers to 1 decimal place.)
B
45.6
A = _________
A = 52°
44.4
B = _________
38
B = _________
C = 90°
C = 90°
c
7.1
a = _________
a
a = 17
b=7
13.3
b = _________
c = 10
21.6
c = _________
A
b
C
Menu
Give exact answers. No calculators!
sin 45 
sin 90 
cos30 
cos0 
sec 60 
csc 30 
tan 45 
tan30 
cot 45 
cot 90 
Menu
Give exact answers. No calculators!
sin 45 
2
cos30 
3
sec 60 
2
sin 90 
1
2
cos0 
1
2
csc 30 
2
tan 45 
1
tan30 
3
cot 45 
1
cot 90 
0




3
Menu
Smallest Positive
Coterminal Angle
Angle
Reference Angle
582º
-260º
sin 30 

cos300 



tan  30 

Menu
Angle
Smallest Positive
Coterminal Angle
582º
222
42
-260º
100
80
Reference Angle
sin 30 
1
cos300 
1




tan  30 

2
2
 3
3
Menu
Angle
Smallest Positive
Coterminal Angle
Reference Angle
200º
-300º
sin 45 


sin 90 
cos  45 
cos180 
tan 225 
tan 270 
Menu
Angle
Smallest Positive
Coterminal Angle
200º
200
20
-300º
60
60
sin 45 



2
cos  45 
2
tan 225 
1
Reference Angle
2
sin 90 
2
cos180 
1
tan 270 
DNE
1
Menu
Smallest Positive
Coterminal Angle
Angle
Reference Angle
11
3
3

4
Degrees
0º
30º
45º
60º
90º
150º
Radians
Menu
Angle
Smallest Positive
Coterminal Angle
Reference Angle
5
3

3
5
4

4
11
3
3

4
Degrees
0º
30º
45º
60º
90º
Radians
0

6

4

3

2
150º
5
6
Menu
1. Find the coterminal angle between 0 and
2 for each of the following:
-5/6
8/3
2. Find the reference angle (between 0 and
/2) for each of the following:
3/4
5/6
3. Give the following trig values:
sin(/6) =
cos(3/4) =
tan(-/3) =
Menu
1. Find the coterminal angle between 0 and
2 for each of the following:
7
-5/6
8/3
2
6
3
2. Find the reference angle (between 0 and
/2) for each of the following:
3/4
5/6


4
6
3. Give the following trig values:
1
sin(/6) =
2
cos(3/4) =
 2
2
tan(-/3) =  3
Menu
4
sin

3
 
cos   
 6
3
tan

4

sec 
cot
3

13
csc

2
Menu
4
sin

3
3
tan

4
sec 
 3
1
1
2
 
cos   
 6
cot

3

13
csc

2
3
3
2
3
1
Menu
sin

3

5
cos

6
11
sin

6
cos
 
sin   
 4
 
cos   
 3

2

5
tan

4
tan  
 
tan   
 6
Menu
sin

3

3
11
sin

6
5
cos

6
2
1
cos
2
  
sin   
 4
2
2

2

3
5
tan

4
2
tan  
0
 
cos   
 3
1
0
 3
1
2
 
tan   
 6
3
Menu
Complete the following identities:
1

sin x
cos x

sin x
cos( x) 
sin( x) 
tan( x) 


tan  x  
2

1  sin 2 x 
1  2 sin 2 x 
cos2 x  sin 2 x 
cos2 x  sin 2 x 
Menu
Complete the following identities:
1

sin x
csc x
cos x

sin x
cos( x) 
cos x
sin( x) 
tan( x) 
 tan x


tan  x  
2

1  sin 2 x 
cos2 x
1  2 sin 2 x 
cos  2x 
cos2 x  sin 2 x 
cos  2x 
cos2 x  sin 2 x 
1
cot x
 sin x
cot x
Menu
Function
Domain
Range
f(x) = sin-1x
g(x) = cos-1x
h(x) = tan-1x
1
sin   
2
1
cos   
2
 1
sin    
 2
tan1 1 
1
1
1
Menu
Function
Domain
f(x) = sin-1x
1, 1
  ,  
2
 2
g(x) = cos-1x
1, 1
0,  
h(x) = tan-1x
 , 
  2 ,  2 
1
sin   
2
1

1
cos   
2

1
6
 1  
sin     6
 2
1
Range
tan1 1 

3
4
Menu
 3

sin 

2


1
1
sin   
2
1

2

sin  

2


1
1

3

cos  

2


tan1 1 
cos1 0 
tan1 0 
1  1 
cos   
2

3

t an  

3


1
Menu
 3

sin 

2


1
1
sin   
2
1


6

3  5
1


tan
1
cos  

6

2


1
3
cos1 0   2

2 
1



1




sin  

cos



4
3

2
2


1

4
tan1 0  0

6

3

t an  

3


1
Menu
 3

arcsin

2


1
arcsin  
2

2

arcsin 

2



3

arccos 

2


arctan 1 
arccos 0 
arctan 0 
1
arccos  
2

3

arct an 

3


Menu
 3 

 5
3
  3 arccos 
  6 arctan 1   4
arcsin

 2 
2




1 
arcsin   6
2
arccos 0   2
arctan 0  0

6



2 
3
1


   4 arccos    3 arct an 

arcsin 



2
3
2




Menu
1. State ONE of the Pythagorean identities.
2. State ONE of the double angle identities.
3. State ONE of the sum/difference identities.
4. Evaluate the following (exact answers without a calculator):
a. sin (7/6) =
b. arctan (-1) =
c. cos -1(-1/2) =
5. Evaluate the following (use a calculator and round to 2 decimal
places):
a. csc (1.8) =
b. cot -1(5) =
c. arcsec (0.3) =
Menu
1. State ONE of the Pythagorean identities.
cos2 x  sin 2 x  1
2. State ONE of the double angle identities. cos(2x)  cos2 x  sin 2 x
3. State ONE of the sum/difference identities.
cos(a  b)  cos a cos b  sin a sin b
4. Evaluate the following (exact answers without a calculator):
1

a. sin (7/6) =
2
b. arctan (-1) =   4
c. cos -1(-1/2) = 2
3
5. Evaluate the following (use a calculator and round to 2 decimal
places):
a. csc (1.8) = 1.03
b. cot -1(5) = 0.20
c. arcsec (0.3) = DNE
Menu
1
sin 0 
1
tan
3
1
1
cos 0 
sin (sin(0.25)) 
1
1
tan 0 
cos(cos 2) 
 3

sin 

2


   
cos  sin    
  4 

2

cos  

2


 1 1 
sin cos  
7

1
1
1
Menu
1
sin 0 
1
cos 0 
1
tan 0 

tan
sin (sin(0.25))  0.25
2
1
cos(cos 2)  DNE
0

     3
cos  sin     4
  4 
1
3

2  3
 4
cos  

2


1
3  3
1
 3

sin 

2


1
1
0
 1 1  48 7  4 3 7
sin cos  
7

Menu
sin
1
1 
cos 1 
1
tan 1 
1
 2

sin 

2


1
 3

cos 

2


1
1


tan  3 
1
tan (tan(0.5)) 
1
sin(sin 3) 
 
cos  sin  
4

1
 1 3 
cos sin

5

Menu
sin
1
1    2
cos 1 

tan 1 

1
1
 2

sin 

2


1
 3

cos 

2


1

1


tan  3 

3
1
tan (tan(0.5)) 
1
sin(sin 3) 
4
0.5
DNE
 
cos  sin  
4

1
4

6
 1 3 
cos sin

5


4
4
5
Menu
Determine the Polar coordinates for the point (-5, 200º) that satisfies the
following criteria:
r > 0 & 0º <  < 360º

(___, ___º)
r < 0 & -360º <  < 0º

(___, ___º)
Convert from Polar to Cartesian:
(0, 120º) = (___, ___)
(7, -45º) = (___, ___)

r = 3sin - 4cos
__________________
Convert from Cartesian to Polar:
(0, 12) = (___, ___º)
(7, -7) = (___, ___º)
2xy = 1

__________________
Menu
Determine the Polar coordinates for the point (-5, 200º) that satisfies the
following criteria:
r > 0 & 0º <  < 360º

(___, ___º)
r < 0 & -360º <  < 0º

(___, ___º)
Convert from Polar to Cartesian:
(0, 120º) = (___, ___)
(7, -45º) = (___, ___)

r = 3sin - 4cos
 5, 20 
 5,
 160

 0, 0
7 2 , 7 2 

2
2 

__________________
x2  y 2  3 y  4 x
Convert from Cartesian to Polar:
(0, 12) = (___, ___º)
(7, -7) = (___, ___º)
2xy = 1

12, 0 
 7,  45    7, 315 
__________________
r  csc(2 )
Menu