Slide 1

7.5 Values of Trig Functions

Trig Values for Non-special Angles
Use calculator to find value & round to 4 digits
* make sure calc is in DEG mode
* angle first or cos first depends on calc
Ex 1)

cos76.5  0.2334

1
Ex 2) cot 295.6 
 0.4791
tan 295.6
Calc doesn’t have cot but has tan

Trig Values for Non-special Angles
Ex 3)

30 o

sin(401 30 )  sin((401  60 ) )
o

Change to
decimal degrees

 sin(401.5 )  0.6626
o

1
Ex 4) csc0.4422 
 2.3368
sin 0.4422
No degree symbol → Radians!!
Change mode on calc

Finding Angles
Ex 5) If 0° ≤ < 360°, find the angle in QI such
that sin   0.6587 , round to nearest tenth degree
angle

trig value

Use inverse sin to find

sin (sin  )  sin (0.6587)
1

1

  sin 1 (0.6587)
  41.2

Ex 6) If 0 ≤ < 360 , find to nearest
tenth of a degree if cos = – 0.9641, QIII

180

First, find the related angle
Change trig value to positive

15.4

QIII

cos   0.9641

   cos (0.9641)
   15.4
  180  15.4  195.4
1

Ex 7) Find in Q IV to nearest tenth
degree such that cot = – 8.028
360
7.1

QIV

1
1
Change to (+)
tan  

cot  8.028 for ref angle
1 
1 
   tan 

 8.028 
   7.1
  360  7.1  352.9

Homework

#716 Pg. 418 1 – 35 odd


Slide 2

7.5 Values of Trig Functions

Trig Values for Non-special Angles
Use calculator to find value & round to 4 digits
* make sure calc is in DEG mode
* angle first or cos first depends on calc
Ex 1)

cos76.5  0.2334

1
Ex 2) cot 295.6 
 0.4791
tan 295.6
Calc doesn’t have cot but has tan

Trig Values for Non-special Angles
Ex 3)

30 o

sin(401 30 )  sin((401  60 ) )
o

Change to
decimal degrees

 sin(401.5 )  0.6626
o

1
Ex 4) csc0.4422 
 2.3368
sin 0.4422
No degree symbol → Radians!!
Change mode on calc

Finding Angles
Ex 5) If 0° ≤ < 360°, find the angle in QI such
that sin   0.6587 , round to nearest tenth degree
angle

trig value

Use inverse sin to find

sin (sin  )  sin (0.6587)
1

1

  sin 1 (0.6587)
  41.2

Ex 6) If 0 ≤ < 360 , find to nearest
tenth of a degree if cos = – 0.9641, QIII

180

First, find the related angle
Change trig value to positive

15.4

QIII

cos   0.9641

   cos (0.9641)
   15.4
  180  15.4  195.4
1

Ex 7) Find in Q IV to nearest tenth
degree such that cot = – 8.028
360
7.1

QIV

1
1
Change to (+)
tan  

cot  8.028 for ref angle
1 
1 
   tan 

 8.028 
   7.1
  360  7.1  352.9

Homework

#716 Pg. 418 1 – 35 odd


Slide 3

7.5 Values of Trig Functions

Trig Values for Non-special Angles
Use calculator to find value & round to 4 digits
* make sure calc is in DEG mode
* angle first or cos first depends on calc
Ex 1)

cos76.5  0.2334

1
Ex 2) cot 295.6 
 0.4791
tan 295.6
Calc doesn’t have cot but has tan

Trig Values for Non-special Angles
Ex 3)

30 o

sin(401 30 )  sin((401  60 ) )
o

Change to
decimal degrees

 sin(401.5 )  0.6626
o

1
Ex 4) csc0.4422 
 2.3368
sin 0.4422
No degree symbol → Radians!!
Change mode on calc

Finding Angles
Ex 5) If 0° ≤ < 360°, find the angle in QI such
that sin   0.6587 , round to nearest tenth degree
angle

trig value

Use inverse sin to find

sin (sin  )  sin (0.6587)
1

1

  sin 1 (0.6587)
  41.2

Ex 6) If 0 ≤ < 360 , find to nearest
tenth of a degree if cos = – 0.9641, QIII

180

First, find the related angle
Change trig value to positive

15.4

QIII

cos   0.9641

   cos (0.9641)
   15.4
  180  15.4  195.4
1

Ex 7) Find in Q IV to nearest tenth
degree such that cot = – 8.028
360
7.1

QIV

1
1
Change to (+)
tan  

cot  8.028 for ref angle
1 
1 
   tan 

 8.028 
   7.1
  360  7.1  352.9

Homework

#716 Pg. 418 1 – 35 odd


Slide 4

7.5 Values of Trig Functions

Trig Values for Non-special Angles
Use calculator to find value & round to 4 digits
* make sure calc is in DEG mode
* angle first or cos first depends on calc
Ex 1)

cos76.5  0.2334

1
Ex 2) cot 295.6 
 0.4791
tan 295.6
Calc doesn’t have cot but has tan

Trig Values for Non-special Angles
Ex 3)

30 o

sin(401 30 )  sin((401  60 ) )
o

Change to
decimal degrees

 sin(401.5 )  0.6626
o

1
Ex 4) csc0.4422 
 2.3368
sin 0.4422
No degree symbol → Radians!!
Change mode on calc

Finding Angles
Ex 5) If 0° ≤ < 360°, find the angle in QI such
that sin   0.6587 , round to nearest tenth degree
angle

trig value

Use inverse sin to find

sin (sin  )  sin (0.6587)
1

1

  sin 1 (0.6587)
  41.2

Ex 6) If 0 ≤ < 360 , find to nearest
tenth of a degree if cos = – 0.9641, QIII

180

First, find the related angle
Change trig value to positive

15.4

QIII

cos   0.9641

   cos (0.9641)
   15.4
  180  15.4  195.4
1

Ex 7) Find in Q IV to nearest tenth
degree such that cot = – 8.028
360
7.1

QIV

1
1
Change to (+)
tan  

cot  8.028 for ref angle
1 
1 
   tan 

 8.028 
   7.1
  360  7.1  352.9

Homework

#716 Pg. 418 1 – 35 odd


Slide 5

7.5 Values of Trig Functions

Trig Values for Non-special Angles
Use calculator to find value & round to 4 digits
* make sure calc is in DEG mode
* angle first or cos first depends on calc
Ex 1)

cos76.5  0.2334

1
Ex 2) cot 295.6 
 0.4791
tan 295.6
Calc doesn’t have cot but has tan

Trig Values for Non-special Angles
Ex 3)

30 o

sin(401 30 )  sin((401  60 ) )
o

Change to
decimal degrees

 sin(401.5 )  0.6626
o

1
Ex 4) csc0.4422 
 2.3368
sin 0.4422
No degree symbol → Radians!!
Change mode on calc

Finding Angles
Ex 5) If 0° ≤ < 360°, find the angle in QI such
that sin   0.6587 , round to nearest tenth degree
angle

trig value

Use inverse sin to find

sin (sin  )  sin (0.6587)
1

1

  sin 1 (0.6587)
  41.2

Ex 6) If 0 ≤ < 360 , find to nearest
tenth of a degree if cos = – 0.9641, QIII

180

First, find the related angle
Change trig value to positive

15.4

QIII

cos   0.9641

   cos (0.9641)
   15.4
  180  15.4  195.4
1

Ex 7) Find in Q IV to nearest tenth
degree such that cot = – 8.028
360
7.1

QIV

1
1
Change to (+)
tan  

cot  8.028 for ref angle
1 
1 
   tan 

 8.028 
   7.1
  360  7.1  352.9

Homework

#716 Pg. 418 1 – 35 odd


Slide 6

7.5 Values of Trig Functions

Trig Values for Non-special Angles
Use calculator to find value & round to 4 digits
* make sure calc is in DEG mode
* angle first or cos first depends on calc
Ex 1)

cos76.5  0.2334

1
Ex 2) cot 295.6 
 0.4791
tan 295.6
Calc doesn’t have cot but has tan

Trig Values for Non-special Angles
Ex 3)

30 o

sin(401 30 )  sin((401  60 ) )
o

Change to
decimal degrees

 sin(401.5 )  0.6626
o

1
Ex 4) csc0.4422 
 2.3368
sin 0.4422
No degree symbol → Radians!!
Change mode on calc

Finding Angles
Ex 5) If 0° ≤ < 360°, find the angle in QI such
that sin   0.6587 , round to nearest tenth degree
angle

trig value

Use inverse sin to find

sin (sin  )  sin (0.6587)
1

1

  sin 1 (0.6587)
  41.2

Ex 6) If 0 ≤ < 360 , find to nearest
tenth of a degree if cos = – 0.9641, QIII

180

First, find the related angle
Change trig value to positive

15.4

QIII

cos   0.9641

   cos (0.9641)
   15.4
  180  15.4  195.4
1

Ex 7) Find in Q IV to nearest tenth
degree such that cot = – 8.028
360
7.1

QIV

1
1
Change to (+)
tan  

cot  8.028 for ref angle
1 
1 
   tan 

 8.028 
   7.1
  360  7.1  352.9

Homework

#716 Pg. 418 1 – 35 odd


Slide 7

7.5 Values of Trig Functions

Trig Values for Non-special Angles
Use calculator to find value & round to 4 digits
* make sure calc is in DEG mode
* angle first or cos first depends on calc
Ex 1)

cos76.5  0.2334

1
Ex 2) cot 295.6 
 0.4791
tan 295.6
Calc doesn’t have cot but has tan

Trig Values for Non-special Angles
Ex 3)

30 o

sin(401 30 )  sin((401  60 ) )
o

Change to
decimal degrees

 sin(401.5 )  0.6626
o

1
Ex 4) csc0.4422 
 2.3368
sin 0.4422
No degree symbol → Radians!!
Change mode on calc

Finding Angles
Ex 5) If 0° ≤ < 360°, find the angle in QI such
that sin   0.6587 , round to nearest tenth degree
angle

trig value

Use inverse sin to find

sin (sin  )  sin (0.6587)
1

1

  sin 1 (0.6587)
  41.2

Ex 6) If 0 ≤ < 360 , find to nearest
tenth of a degree if cos = – 0.9641, QIII

180

First, find the related angle
Change trig value to positive

15.4

QIII

cos   0.9641

   cos (0.9641)
   15.4
  180  15.4  195.4
1

Ex 7) Find in Q IV to nearest tenth
degree such that cot = – 8.028
360
7.1

QIV

1
1
Change to (+)
tan  

cot  8.028 for ref angle
1 
1 
   tan 

 8.028 
   7.1
  360  7.1  352.9

Homework

#716 Pg. 418 1 – 35 odd