Pre Calculus
Verifying Identities and Solving Trigonometric Equations
Name _____________________
Assignment # _______
COMPLETE ALL OF YOUR WORK ON A SEPARATE PIECE OF PAPER.
I.
1.
3.
5.
Verify the following identities.
cos θ
1 − sin θ
−
cos θ
1 + sin θ
sin4 x − cos4 x
2
2 sin x − 1
= 2 tan θ
=1
(sec x − tan x )2 + 1
csc x (sec x − tan x )
2.
4.
= 2 tan x
6.
1 + sin φ
cos φ
=
cos φ
1 − sin φ
cos(−x )
sin(−x ) cot(−x )
cot2 x
csc x − 1
=
=1
1 + sin x
sin x
II. Solve on the interval [0, 2 π ). Be exact when possible; otherwise, round to the
nearest hundredth. Show work.
7. 2 cos x + 3 = 0
8. sin2x = −1
9. cot 2θ = 4
10. 4 tan 3θ − 4 = 0
11. 9 sin x − 1 = sin x + 2
12. 3 tan x sin x + sin x = 0
III. Solve the following equations. Give the general solution. Show work.
13. tan2 3x = 3
15.
14. 2 sin2 x − 5 sin x − 3 = 0
( )
2 sin x cos 2x − 3 sin x = 0
16. 2 cos2 2x + cos 2x − 1 = 0
IV. Solve using the quadratic formula. Solve on the interval [0, 2 π ). Round
answers to the nearest hundredth. Show work.
17. tan2 x − 8 tan x + 13 = 0
18. 2 cos2 x = 1 − 2 sin x