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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IV. Can You Use the Sum and Difference Formulas to Establish Identities?<br />
24) Establish the identity<br />
cos( x ) cos x sin x .<br />
3 1<br />
6 2 2<br />
25) Establish the identity cos( x y ) 1 tan x tan y<br />
.<br />
cos( x y) 1 tan x tan y<br />
V. Can You Use the Sum and Difference Formulas to Evaluate Functions Involving Inverse<br />
Trigonometric Functions?<br />
1 1 3<br />
26) Find the exact value of this expression sin cos 1 sin .<br />
2 2<br />
27) Write the trigonometric expression<br />
u and v.<br />
cos sin<br />
u<br />
cos<br />
1 1<br />
v as an algebraic expression containing<br />
VI. Can You Use Double-angle and Half-angle Formulas to Evaluate Trigonometric Functions<br />
and Prove Identities?<br />
A. Use Double-angle Formulas to Find Exact Values.<br />
28) Find cos(2θ) given that sin θ = 15<br />
17 , 0 < θ < π/2.<br />
29) Find cos(2θ) given that cos θ = 1<br />
3<br />
, csc θ < 0.<br />
4<br />
30) Find sin(2θ) given that sin θ =<br />
5<br />
, 3π/2 < θ < 2π.<br />
31) Find the exact value of the expression<br />
1 2<br />
sin 2sin<br />
2<br />
.<br />
B. Use Double-angle Formulas to Establish Identities.<br />
2<br />
csc<br />
32) Establish the identity sec(2 ) .<br />
2<br />
csc 2<br />
33) Establish the identity sin(4x) = (4 sin x cos x)(<br />
C. Use Half-angle Formulas to Find Exact Values.<br />
2<br />
2cos x 1).<br />
34) Find cos ( 2<br />
) given that sin θ = 1 4<br />
and tan θ > 0.<br />
35) Find sin ( 2<br />
) given that csc θ = 6 and cos θ > 0.<br />
36) Find tan ( 2<br />
) given that tan θ = 3, π < θ < 3π/2.<br />
REV 12/01/2010 3
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