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Precalculus Final Exam REVIEW 4
Name:_________________________________Hour: _____
NO CALCULATOR allowed on this section!
Recognize and use the appropriate TRIGONOMETRIC IDENTITY to SIMPLIFY the expression COMPLETELY. Use Ch 10 notecard!
75.
1  cos 50
2
79.
22.5° −
83.
°
76. 2
22.5°
°
°
80. s 45°
77.
−1
15° −
45°
15°
84. 1 − 2sin 75°
2 sin 165 cos 165
81.
78.
°
82. cos 9 cos 3 − sin 9 sin 3
85. sin(30° + ) + sin(30° − )
86.
°
°
1  cos 50
2
NO CALCULATOR allowed on this section!
Use the appropriate trigonometric identity to evaluate the expression. Rationalize when necessary.
87. Use the sum and difference identities to find the EXACT
value of sin 75 .
88. Use the sum and difference identities to find the EXACT
value of cos 15 .
89. Use the sum and difference identities to find the EXACT
value of tan 195 .
90. Use the HALF-ANGLE formula to find the EXACT
value of:sin 15°.
CALCULATOR allowed on #91-100.
91. GIVEN:
sin α = cos
and 0 <
= and <
<
sin α = cos
= and <
cos
< 2π
Use the sum and difference identities to find: tan(
93. GIVEN:
+ )
<2
and 0 <
<
− )
94. Use the double angle identities to find the sin 2 if
<
 3
and
2
<2
Use the sum and difference identities to find: sin(
=
and <
Use the sum and difference identities to find: cos(
cos  
and <
tanα = 92. GIVEN:
    2 .
+ )
95. Use the double angle identities to find the cos 2 if
= 2 and 0     .
96. Use the double angle identities to find the tan 2 if
csc  
13
where 90    270 .
5
97. Use a double angle formula to SOLVE:
3 (2 ) = 2 − cos for all x-values such that 0  x  360 .
98. Use a double angle formula to SOLVE:
( 2 ) =
for all x-values such that 0 ≤
99. Use a double angle formula to SOLVE:
cos(2 ) =
for all x-values such that 0 ≤
100. SOLVE the following double angle equation:
<2 .
(2 ) =
√
<2 .
for all x-values such that 0  x  360 .