Name______________________________
Math 1316.3S7
Prof. Merrill
Lab 3--Trig Solving and Simplifications
Simplify the following expressions. Circle answers!
1. cot x sin x
2.
4. cos x  sin x tan x
6.
af
af
sin  x
cos  x
cos 2 x
 sin x
sin x
3.
1  cos 2 x
cos 2 x
5. sin2 x  tan2 x  cos2 x
7.
 sin x  cos x  sin x  cos x 
sin 2 x 
1
sec2 x
3
F
I
 x Jif tan x = ½
G
H4 K
F  x I  cosF  x I
H3 K H3 K
8. cos
9. Evaluate tan
10. Find tan 345 in simplest radical form.
For 11-12: 0   
11. sin 2

2
and sin  =
1
, evaluate:
3
12. cos 2
Simplify:
13. cos2
Fx I - sin Fx I
H2 K H2 K
2
14.
sin 2x
1  cos 2x
15. Solve: 2 sin 2x = 2 cos x
for 0  x < 2
16. Solve: sin 2x = cos 2x
for 0  x < 2
18. Find cos 2 given cot  = 2,
 lies in QIII.
5
and  lies in QII,
13
find the exact value of tan 2.
17. If sin  
19. Solve: 3 sin x – 2 = 5 sin x - 1
Rewrite each expression without double angles. Simplify.
20.
cos 2 x
cos x
21.
sin 2 x
2 sin x
22. 2csc 2x
23. cos 2x + sin x
Solve the equation for 0 ≤ x < 2π
24. cos 2x = -sin x
25. cos 2x + cos x = 0
26. sec 2x = 2
27. sin 2x  2 sin x  0
Find the exact value of the expression in 28-30—Use Half-Angle Formulas.
5
28. sin
29. cos 67.5o
8
30. tan 112.5o
31. A batted baseball leaves the bat at an angle of θ with the horizontal, with a velocity
of vo = 100 feet per second, and is caught by an outfielder. If sinθ = 0.60, first find the
distance the ball was hit and then check your answer by finding θ. Remember that
1 2
r
vo sin 2 , where r is the horizontal distance traveled.
32
Solve each of the following from 0  x  2 :
32.
2cos2 x  cosx  0
33.
sin2 x  1 0
34.
2sin2 x  sinx  1  0
35.
tanx  2sinx
36.
sinx  cscx
37.
sin2 x  2cosx  2
Use your identities to simplify each expression as much as possible.
38. cos 95º cos 20º - sin 95º sin 20º =




39. sin cos  cos sin 
4
2
4
2
40.
tan

2
1  tan
 tan

2

tan
3 =

3
Prove the following.
41.
sec x  csc x
 csc x
1  tan x
42.
cos
1  sin

 2 sec 
1  sin
cos 
43. (sin x + cos x)2 cot x = cot x + 2 cos2x
44. Suppose sin A =
a) sin(A + B) =
b) cos(A + B) =
c) tan(A + B) =
4
5
and tan B = 
3

, where
 A  B   . Find …
4
2