2/7/2014
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Assessment Results » Sum and Difference Identities for Sine and
Cosine
Individual Report: Gregory Snakard
Student
Snakard, Gregory
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1. What is the best first step if your plan is to find the exact value of cos 75° using the Cosine Angle Sum
Identity?
A. cos (30° + 45°)
B. cos (60° + 15°)
C. cos (37.5° + 37.5°)
D. cos (120° - 45°)
Correct Answer: A — cos (30° + 45°)
Explanation: The best first step is to rewrite 75° as the sum of 30° and 45°. The problem with using
(60° + 15°) or (37.5° + 37.5°) is that you do not know the exact values of the trigonometric functions for
15° or 37.5°. The problem with using (120° - 45°) is that this would lead to using a difference identity, not
a sum identity. So, the best choice is cos (30° + 45°).
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2. What could be the second step in finding the exact value of sin 105°?
A. sin 60° cos 45° – cos 60° sin 45°
B. sin 60° cos 45° + cos 60° sin 45°
C. cos 60° cos 45° – sin 60° sin 45°
D. cos 60° cos 45° + sin 60° sin 45°
Correct Answer: B — sin 60° cos 45° + cos 60° sin 45°
Explanation: The first step would be to rewrite 105° as the sum of 45° and 60°, making sin 105° = sin
(45° + 60°). The second step would be to use the sum identity for sine:
sin (45° + 60°) = sin 60° cos 45° + cos 60° sin 45°
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3. What is cos 10° cos 8° − sin 10° sin 8° equal to?
A. sin 18°
B. sin 2°
C. cos 18°
D. cos 2°
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2/7/2014
Assessment Results | ExploreLearning
Correct Answer: C — cos 18°
Explanation: cos 10° cos 8° − sin 10° sin 8° = cos 18°. This is the Cosine Angle Sum Identity. The two
angles that appear in the identity are 10° and 8°, so the expression is equal to the cosine of the sum of
these two angles, or cos (10° + 8°).
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4. Which expression is equal to cos 15°?
A. sin 37° cos 22° - cos 37° sin 22°
B. sin 37° cos 22° + cos 37° sin 22°
C. cos 37° cos 22° - sin 37° sin 22°
D. cos 37° cos 22° + sin 37° sin 22°
Correct Answer: D — cos 37° cos 22° + sin 37° sin 22°
Explanation: Since the angles being used are 37° and 22°, and you want to find cos 15°, you want to use
the Cosine Angle Difference Identity. The expression that is an instance of the Cosine Angle Difference
Identity is cos 37° cos 22° + sin 37° sin 22°.
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5. True or false? sin 45° cos 30° − cos 45° sin 30° = sin 60° cos 45° − cos 60° sin 45°.
A. TRUE
B. FALSE
Correct Answer: A — TRUE
Explanation: It is true that sin 45° cos 30° − cos 45° sin 30° = sin 60° cos 45° − cos 60° sin 45°. Both
expressions are instances of the Sine Angle Difference Identity. The first expression is equal to
sin (45° − 30°), which equals sin 15°. The second expression is equal to sin (60° − 45°), which also
equals sin 15°. Therefore, the two given expressions are equal.
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