Review for Chapter 5 Test Name: ______________________ Trig Unit 1 Show all work for credit. Simplify all answers (in radical form, if appropriate). Sketch angles and label the quadrant. Remember to include the rotation arrow.

1.

3π4

2. –135

3.

7π5

4. 200

5. − 7π

11 6. –520

Convert degrees to radians and radians to degrees.

7.

3π10

8. − 2

5π

9. 160 10. –280

Find the arc length and sector area (MEMORIZE THE FORMULAS!) 11. If r = 14 inches and s = 6π , find the central angle θ .

12. If A = 9 mi2 and θ =

3π4 radians, find the area of the sector.

13. The minute hand of a clock is 4 inches long. How far does the tip of the minute hand move in 35 minutes?

14. A water sprinkler sprays water over a distance of 8 feet while rotating through an angle of 100° . What area of the lawn receives water?

State which quadrants satisfy the criteria described. 15. sine and cosecant are negative 16. tangent and cotangent are

negative

17. sin θ( ) >0 and

sec θ( ) <0 18.

cot θ( ) <0 and

csc θ( ) >0

Use even and odd properties to find the value of each expression. 19. sec (–60

) 20. sin

− 7π

6⎛

⎝⎜⎞

⎠⎟

21. cot – 3π

4⎛⎝⎜

⎞⎠⎟

22. cos (– 5π )

Find the exact value of each expression.

23. sinπ3 − cosπ

24. 2cos 3π

4⎛

⎝⎜⎞

⎠⎟−6tan −π3

⎛

⎝⎜⎞

⎠⎟

25. csc −π3

⎛

⎝⎜⎞

⎠⎟+ cos 3π( )

26. 6cot 2π

3⎛

⎝⎜⎞

⎠⎟− 2csc −π3

⎛

⎝⎜⎞

⎠⎟

27. tan(20)− sin20

cos(20) 28.

sin 70( )cos(−430) + tan(−70)

29. tan −3π

8⎛

⎝⎜⎞

⎠⎟cot −11π

8⎛

⎝⎜⎞

⎠⎟ 30.

sec −π9

⎛

⎝⎜⎞

⎠⎟cos 37π

9⎛

⎝⎜⎞

⎠⎟

31. Eval trig functions (all types of angles)

a. sin

π4

b. cos

5π6

c. tan −90( )

d. tan

11π4

e. sin − 3π

2 f. tan

5π2

g. sin − 5π

3 h.

sin 120( ) i. sec

−π

2⎛⎝⎜

⎞⎠⎟

j. cot −13π

3 k. sin

15π6

l. tan

5π3

m. cot

12π6

n. sec − 7π

4 o. csc

31π6

p. cot − 5π

6 q. csc

−17π

6⎛⎝⎜

⎞⎠⎟

r. csc − 4π

3

Find the six trig functions for the given angle θ .

32. θ = −π

6

sin θ = ______ csc θ = ______ cos θ = ______ sec θ = ______ tan θ = ______ cot θ = ______

33. θ = −5π

2

cos θ = ______ sec θ = ______ cot θ = ______

Find the six trig functions that correspond to the point, P, on a circle. 34. P = (5, –4)

sin θ = ______ csc θ = ______ cos θ = ______ sec θ = ______ tan θ = ______ cot θ = ______

35. P = (–3, –2) sin θ = ______ csc θ = ______ tan θ = ______

Find the exact value of the remaining trig functions if:

36. cosθ = − 3

5 and cotθ < 0

sin θ = ______ cos θ = ______ csc θ = ______ sec θ = ______ cot θ = ______

37. tan θ =

37

and cos θ < 0

sin θ = ______ cot θ = ______ sec θ = ______ csc θ = ______ tan θ = ______

#1 Function: f (x)= 2sin x− π2

⎛

⎝⎜⎞

⎠⎟

#2 Function: f (x)= −cos x

2 + π2⎛

⎝⎜⎞

⎠⎟− 4

#3 Function: f (x)= −3tan 4x+3π( )+1

Amplitude: _________

Period: _______

Unit: ______

Phase Shift: ________

Vertical Shift: _______

Domain: ___________

Range: __________

Amplitude: _________

Period: _______

Unit: ______

Phase Shift: ________

Vertical Shift: _______

Domain: ___________

Range: __________

Amplitude: _________

Period: _______

Unit: ______

Phase Shift: ________

Vertical Shift: _______

Domain: ___________

Range: __________

#4 Function: f (x)= −csc 3x( )− 2

#5 Function: f (x)= −2sec x+π( )

#6 Function: f (x)= cot 2x− 3π

4⎛

⎝⎜⎞

⎠⎟−1

Amplitude: _________

Period: _______

Unit: ______

Phase Shift: ________

Vertical Shift: _______

Domain: ___________

Range: __________

Amplitude: _________

Period: _______

Unit: ______

Phase Shift: ________

Vertical Shift: _______

Domain: ___________

Range: __________

Amplitude: _________

Period: _______

Unit: ______

Phase Shift: ________

Vertical Shift: _______

Domain: ___________

Range: __________

Sketch a graph of each function 7. f (x)= sin(θ)−1

8. f (x)= sin(θ +π )

9. f (x)= cos(θ)+1 10. f (x)= cos(θ −π )

11. f (x)= −sin(θ)+1 12. f (x)= −cos(θ)+1

Write each graph with a sine function and cosine function. 7. 8.

9. 10.