Trigonometric Functions of Any Angle Date - Precalculus

PCM 40S - Chapter 2

Name___________________________________

Trigonometric Functions of Any Angle

ID: 1

Date________________

Use the given point on the terminal side of angle ¦È to find the value of the trigonometric

function indicated.

1) tan ¦È ; (3, 4)

2) sec ¦È ; (?2, ?2 3 )

3) cos ¦È ; (2, ? 5 )

4) cot ¦È ; (? 17, 8)

5) sin ¦È ; ( 13, ?6)

6) csc ¦È ; (?4, ?2 5 )

Find the exact value of each trigonometric function.

7) sin ?

3¦Ð

2

8) csc ?

9) cos ?

7¦Ð

6

10) cot

11) tan ?

¦Ð

6

¦Ð

4

4¦Ð

3

12) sec ?

5¦Ð

3

State the quadrant in which ¦È lies.

13) sin¦È < 0 and cos¦È < 0

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14) sin¦È > 0 and cos¦È > 0

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15) sin¦È > 0 and tan¦È < 0

16) sec¦È > 0 and cot¦È < 0

Find the values of the six trigonometric functions of ¦È given the constraint on the angle.

15

; sin¦È < 0.

8

3

17) sin¦È = ; ¦È lies in Quadrant II.

5

18) tan¦È = ?

19) cot¦È = ?3; cos¦È > 0.

20) sin¦È = 0; sec¦È = ?1.

Solve each equation for 0 ¡Ü ¦È < 2¦Ð .

21) ?

3

= cos ¦È

2

23) tan ¦È = 0

22) ?

1

= sin ¦È

2

24) sin ¦È = 0

Evaluate without using a calculator. Keep in mind the domain of the inverse function.

25) sin

?1 1

2

27) tan

29) sin

26) cos

?1

?1

3

3

3

2

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?1 1

2

?1

28) tan ? 3

?1

30) cos ?

-2-

1

2

Worksheet by Kuta Software LLC

Answers to Trigonometric Functions of Any Angle (ID: 1)

1)

2) ?2

4

3

4) ?

17

8

5) ?

7) 1

3)

6

7

3 5

5

3

9) ?

2

12) 2

6) ?

8) ? 2

3

3

13) III

16) II

10)

11) ?

2

3

3

3

14) I

15) II

4

3

5

4

5

17) cos¦È = ? ; tan¦È = ? ; csc¦È = ; sec¦È = ? ; cot¦È = ?

5

4

4

3

3

15

15

17

8

8

17

18) sin¦È = ? ; cos¦È = ; tan¦È = ? ; csc¦È = ? ; sec¦È = ; cot¦È = ?

17

8

15

15

17

8

1

10

10

10

19) sin¦È = ?

; cos¦È = 3 ?

; tan¦È = ? ; csc¦È = ? 10; sec¦È =

; cot¦È = ?3

10

10

3

3

20) sin¦È = 0; cos¦È = ?1; tan¦È = 0; csc¦È is undefined; sec¦È = ?1; cot¦È is undefined

23) {0, ¦Ð }

5¦Ð 7¦Ð

7¦Ð 11¦Ð

,

22)

,

21)

6 6

6

6

24) {0, ¦Ð }

¦Ð

¦Ð

25)

26)

6

3

¦Ð

¦Ð

¦Ð

27)

28) ?

29)

6

3

3

2¦Ð

30)

3

{

}

{

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}

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Worksheet by Kuta Software LLC

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