C H A P T E R 5 Analytic Trigonometry

450 Chapter 5 Analytic Trigonometry
123.
Sketch the graph of y first.
1
f x
cosx
2 1
secx
2 4
124.
Amplitude:
Period:
2
One cycle:
1
2
The x-intercepts of correspond to the vertical asymptotes of f x .
1
y secx
2 1
cosx
2
x 5
, x , . . .
4 4
Vocabulary Check
x
0 ⇒ x
4 4
x
7
2 ⇒ x
4 4
f x 3
cosx 3
2
2
1. identity 2. conditional equation
3. tan u 4. cot u
5. cos 6. sin u
2 u
7. csc u
8. sec u
4
4
3
Using so the amplitude is
2 .
3
y a cos bx, a
2
b 1 so the period is 2.
1
x shifts the graph right by and 3 shifts the graph upward by 3.
1. sin t csc t sin t 1
sin t 1 2. sec y cos y 1
cos y 1
cos y
3. 1 sin 1 sin 1 sin 2 cos 2
Section 5.2 Verifying Trigonometric Identities
4
3
2
1
π
2
−2
−3
−4
y
3π 2π
2
4
4. cot 2 ysec 2 y 1 cot 2 y tan 2 y 1
x
5
4
3
1
−2
−3
y
−π
π 2π
−1
■ You should know the difference between an expression, a conditional equation, and an identity.
■ You should be able to solve trigonometric identities, using the following techniques.
(a) Work with one side at a time. Do not “cross” the equal sign.
(b) Use algebraic techniques such as combining fractions, factoring expressions, rationalizing denominators, and squaring
binomials.
(c) Use the fundamental identities.
(d) Convert all the terms into sines and cosines.
x