Chapter 5 – Trigonometric Identities
Review Sheet
1. Use the given values and trig identities to
evaluate all six trig functions.
4 5


csc   x   9
sin x 
9
2

2. Use identities to simplify the
expression.
tan 2  csc 2   tan 2 
cot 2  sin 2 
3. Simplify
1
1

csc   1 csc   1
4. Verify the Identity
sin5 x cos2 x  (cos2 x  2cos4 x  cos6 x)sin x
5. Find all the solutions on the interval
[0, 2 ]
cos 4 x(cos x  1)  0
6. Find all the solutions:
2sin 2 x  2  0
7. Find the sine, cosine, and tangent of the
angle by using a sum or difference
25
formula.  
12
8. Find the sine, cosine, and tangent of the
angle by using your half-angle
identities.
25

12
9. Factor and simplify:
sec 4 x  tan 4 x
sec 2 x  tan 2 x
10. Verify the identity
cos
1
2
x sin x  cos
5
2
x sin x  sin 3 x cos x
11. Find all the solutions in the interval from [0, 2 ] .
tan
x
 sin x  0
2
12. Determine whether or not this statement is
true or false. Justify your answer (give a
counterexample).
13. Find all of the solutions in the interval
[0, 2 ] : tan 2 x  tan x  0
sin( x  y )  sin x  sin y
14. Simplify the expression
sin 4
1  cos 4
15. The point (3,4) is on the terminal side of an
angle  . Find the sine, cosine, and tangent
of 2 .