MATH 175: Chapter 7 Review Analytic Trigonometry - The Learning ...
MATH 175: Chapter 7 Review Analytic Trigonometry - The Learning ...
MATH 175: Chapter 7 Review Analytic Trigonometry - The Learning ...
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II. Trigonometric Identities<br />
A. Can You Use Algebra to Simplify Trigonometric Expressions?<br />
12) Multiply and simplify the expression<br />
(tan 1)(tan 1)<br />
2<br />
sec<br />
tan<br />
.<br />
B. Can You Use the Basic Identities to Establish Other Identities?<br />
2<br />
13) Establish the identity: (sin x)(tan x cos x - cot x cos x) = 1-2 cos x .<br />
14) Establish the identity.<br />
cos u 1<br />
cos u sin u 1 tan u .<br />
cosu<br />
15) Establish the identity. sec u + tan u =<br />
1 sin u .<br />
sin x sin x<br />
16) Establish the identity.<br />
1 cos x 1 cos x<br />
2csc x .<br />
III. Can You Use the Sum and Difference Formulas to Find Exact Values of Trigonometric<br />
Functions?<br />
11<br />
17) Find the exact value of the expression sin(<br />
12<br />
) .<br />
18) Find the exact value of the expression tan 75°.<br />
o<br />
o<br />
tan 65 tan85<br />
19) Find the exact value of the expression<br />
o o .<br />
1 tan 65 tan85<br />
20) Find the exact value of the expression cos (5π/18) sin (π/9) - cos (π/9) sin (5π/18).<br />
21) Find the exact value of cos (α + β) under the given conditions.<br />
sin α =<br />
20<br />
29 , 0 < α < (π/2); cos β 12<br />
13 , 0 < β < (π/2).<br />
22) Find the exact value of sin (α + β) under the given conditions.<br />
15<br />
tan α , π < α < (3π/2); cos β 24<br />
8 25<br />
, π/2 < β < π.<br />
1<br />
23) If sin θ = , θ in quadrant II, find the exact value of 4<br />
cos(<br />
6) .<br />
REV 12/01/2010 2
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