Infinite Precalculus - Trigonometric Functions

Precalculus

Name___________________________________

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Trigonometric Functions

Date________________ Period____

Verify each identity.

1) -sin xsec x = -tan x

2) tan2 x - cot2 x = sec2 x - csc2 x

3) tan2 x + csc2 x = sec2 x + cot2 x

1

sin x

4)

=

csc x + 1 sin x + 1

cos2 x

1

5)

=

sin2 x sec2 x - 1

6)

1

= cos xcsc2 x

sec xsin2 x

Worksheet by Kuta Software LLC

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Find the exact value of each expression without using a calculator.

7) tan-1 - 3 3

8) cos-1 - 3 2

9) cos-1 -1

10) sin-1 - 1 2

( ) 11)

cos-1

p csc

2

12) sec sin-1 15 4

13) tan-1 (cos p)

( ) 14)

sin-1

p tan -

4

15) sec cos-1 8 17

16) tan sin-1 5 5

17) csc tan-1 3

( ) 18)

cos-1

p cot

2

Write each trigonometric expression as an algebraic expression.

19) cot cos-1 x

20) cot sin-1 1 x

21) sec sin-1 2x

22) sec tan-1 3x

Worksheet by Kuta Software LLC

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Find the amplitude, the period in radians, the phase shift in radians, and the vertical shift. Then sketch the graph using radians.

( ) q p

23) y = 4sin + - 1 2 3

( )p

24) y = 3cos q + 3

25) y = 2cos 4q + 1

26) y = -2 + 3sin 2q

( )5p

27) y = tan 2q + 4

q 28) y = 3tan - 1

3

Worksheet by Kuta Software LLC

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Find the exact value of each trigonometric function without using a calculator.

9p 29) sin -

4

8p 30) cot -

3

17p 31) tan

3

11p 33) tan -

4

23p 35) csc -

4

5p 32) sec -

3

16p 34) sin

3

9p 36) cos -

4

Use the given point on the terminal side of angle q to find the value of the trigonometric function indicated.

37) csc q ; (-3, -2)

38) sec q ; (-2 3, -2)

39) cos q ; ( 15, -7)

40) tan q ; (-9, - 19)

41) sin q ; (2, -11)

42) cot q ; (-2 5, 4)

Worksheet by Kuta Software LLC

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