Pre – Calculus Day 81 Final Exam Review Trigonometry
Solve the equations for
Name ______________________________
0 ≤ x < 2π
1.
2 cos x + 1 = 0
2.
csc2 x − 2 = 0
3.
3csc2 x − 4 = 0
4.
2 sin2 2 x = 1
5.
sec2 x − sec x = 2
6.
(3tan
7.
tan2 x − 1 = 0
8.
3tan3 x = tan x
2
x − 1 tan2 x − 3 = 0
)(
)
Verify the following trig identities
9.
sin 2 x
cos x +
= sec x
cos x
11.
cos x
1 + sin x
=
1 − sin x
cos x
10. cos x + tan x sin x = sec x
12.
1 + tan2x = sec2x
sec x
= sin x
13. cot x + tan x
14. Sin4x – cos4x = 2sin2x - 1
Simplify the following trigonometric expressions to the most simplified version.
15.
!
𝑡𝑎𝑛𝜃𝑐𝑜𝑠𝜃 + 𝑐𝑠𝑐𝜃𝑠𝑖𝑛 𝜃
17. cos 𝑥 sec 𝑥 −
19. sec(x)cot(x)
𝑐𝑜𝑠 ! (𝑥)
16.
!"#$!!"#$!"#! !
18.
!"# (!)!"#! ! !!"# ! (!)
20.
!!"#$%&!$
!"# (!)
!"#! !
!!!"#$