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MATH 1112A
Test 2 Study Guide
Part 1: Calculating Trigonometric Function Values using Identities
a) Sum & Difference Identities
b) Double/Half Angle Identities
c) Inverse Trig Functions
d) Composition of Functions
Examples: Use identities and inverse trigonometric functions to calculate the exact
values (NO decimals!) of each of the function values below.

4
sin(arcsin( ))
5
cos( )
12
sin(2 cos 1 (
20
))
29
tan(cos 1 (
1
3
cos(arccos( )  arcsin( ))
2
2
Part 2: Simplify Trig Expressions
Examples: Simplify each of the following trigonometric expressions. Show all of your
work.
(1  sin x)(sec x  tan x)
sec x  cos x
tan x
Part 3: Prove Trig Identities:
Examples: Show all work and use correct logical structure.
sin( x  y )  sin( x  y )  2 cos x sin y
sin(u  v)
cos u cos v
1  sin 2
1
 1  sec  csc 
sin 2
2
tan u  tan v 
Part 4: Solve Trig Equations:
Examples:
a) Find the solutions on the interval [0,2π)
tan 2 x  tan x
b) Find all solutions
2cos x 1  0
5sin  3  3
8
))
17
Part 5: Miscellaneous
1. If A and B are positive acute angles, sin A 
of sin( A  B ) ?
16
a) 
65
2.
b)
33
65
c)
5
4
, and cos B  , what is the value
13
5
56
65
d)
63
65
12
3
, cos y  , and x and y are acute angles, what is the value of
13
5
cos( x  y ) ?
33
14
21
63
a) 
b) 
c)
d)
65
65
65
65
If sin x 
5
, what is the value of sin 2 ?
13
60
120
c)
d)
169
169
3. If  is an acute angle such that sin  
a)
10
26
b)
12
13
4. The expression (1  cos x)(1  cos x) is equivalent to
a) 1
b) sin 2 x
5. The expression
a) sin
6. The expression
a) sin
7. The expression
a)
cos 2 
sin 
c) sec2 x
d ) csc2 x
2 cos 
is equivalent to
sin 2
b) sec
c) csc
d ) cot
sec 
is equivalent to
csc 
b) cos
c) tan
d ) cot
tan 
is equivalent to
sec 
sin 
b)
c) sin
cos 2 
d ) cos
8. The expression cos 40 cos10  sin 40 sin10 is equivalent to
a) cos30
b) cos50
c) sin30
d ) sin50
9. What value of x in the interval 0  x  180 satisfies the equation 3 tan x  1  0?
a)  30
b) 30
c ) 60
d ) 150
Resource: New York Math B Regents