Review 5.3 – 5.5 Worksheet Name: _______________________________________________ Solve the following equations in the interval [ 0, 2π ).

1. sin x = 3-sin x

4. 2cos2 x -cosx =1

7. sin x +p

4( )-sin x -p4( ) =1

2. 0.5secx -1=0

5. sin2 x -2sin x =0

3. sinxcosx =3cosx

6. cos2 x +sin x =1

Verify the following. Be sure to show all steps and work when dealing with quadrant angles.

8. cos x +p

2( ) = -sin x 9. 2cos2 x = cos2x +1

Find the exact value of the following.

10. cos11.25°cos33.75°-sin11.25°sin33.75° 11.

tan5p36

+ tan11p18

1- tan5p36

tan11p18

12. 15°=60°-45° 13. 25p

12=11p

6+p

4

Find sin 15° and cos 15° Find tan25𝜋

12

Find the exact value of the trigonometric function given that sinu = 3

4 and

cosv = -5

13 .

Assume both u and v are in Quadrant II.

14. sin(u+ v)

Find the exact values of the sine, cosine, and tangent of the angles below using half-angle formulas.

15. -75° 16. 7p

12

Find the exact values of the sin 2x, cos 2x, and tan 2x using the information below.

17. sin x = -4

5,p < x <3p

2

Find the exact values of the sin x/2, cos x/2, and tan x/2 using the information below.

18. cosx = -2

7,p

2< x <p

State whether each of the following are true or false. Explain why.

19 a. If p

2< x <p then

cos x

2( ) <0 19 b. sin (x + y) = sin x + sin y