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Name
LESSON
Date
Class
Practice A
14-3 Fundamental Trigonometric Identities
Prove each trigonometric identity.
sin
csc 1. _________
1 cos 2 sin ____________________
a. Modify the left-hand side. Replace 1
with a known identify.
cos 2 sin 2 cos 2
sin _____
sin 2 1
____
csc ; csc csc sin b. Simplify the denominator.
c. Keep simplifying and substituting identities
until the left side matches the right side.
2. cos 4 cos 2 sin 2 sin 2 1
4
2
2
2
cos cos sin sin 1
cos 2 cos 2 sin 2 sin 2 1
cos 2 cos 2 sin 2 sin 2 1
cos 2 1 sin 2 1
cos 2 sin 2 1
11
csc 3. cot _____
sec 1
____
csc sin cot _____; cot _____;
sec 1
_____
cos cos cot _____; cot cot sin Rewrite each expression in terms of cos . Then simplify.
cot 4. ______
2 csc a. Rewrite each function in terms of sin or cos .
b. Rewrite the fraction in simplest form.
5. sin cot sin cot cos sin • _____ sin cos cos 2 ____________
6. cos
sin 2 cos
cos 2
____________
sin 2 2
cos
cos ____________
1 cos 2
cos 1 cos ____________________
1 cos 1 cos cos ________
1 cos cos _____
sin _____
2
____
sin sin cos _____
cos _________
2sin 2
2 cos ______________
7. sin
sec 2 tan 2 2
sin
2cos 2
_____________
sec 2 tan 2
2
2
1 cos 2cos __________________
1 sec 2 1 ______
2
cos 1 cos 2
_________________
1 ______
1 1
______
cos 2 cos 2
2
2
2
1 cos Solve.
8. Use the equation mg sin mg cos to determine the
angle at which a desk can be tilted before a paperback
book on the desk begins to slide. Assume 1.11.
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
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Holt Algebra 2
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1/3/06 4:41:49 PM
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