C H A P T E R 5 Analytic Trigonometry

Section 5.1 Using Fundamental Identities 449
113. Let x, y be any point on the terminal side of .
114. Divide both sides of by cos2 sin :
2 cos2 1
Then, r x and
2 y2 sin 2 cos 2 y
r 2
x
r 2
y2 x 2
r 2
r2
r 2
1.
115. x 5x 5 x 2 5 2 x 25 116.
117.
119.
121.
1 x x 8 xx 5
x 5 x 8 x 5x 8
x2 6x 8
x 5x 8
2x
x2 7
4 x 4 2xx 4 7x2 4
x2 4x 4
f x 1
2 sinx
Amplitude:
Period:
2
Key points:
1
2
2
2x2 8x 7x 2 28
x 2 4x 4
5x2 8x 28
x 2 4x 4
0, 0, 1 1
,
2 2 , 1, 0, 3
, 1 , 2, 0
2
2
2
1
−1
−2
y
1 3
x
118.
120.
sin2
cos2 cos2
cos2 1
cos2
tan 2 1 sec 2
Divide both sides of by sin2 sin :
2 cos2 1
sin2
sin2 cos2
sin2 1
sin2
1 cot 2 csc 2
Discussion for remembering identities will vary, but one
key is first to learn the identities that concern the sine
and cosine functions thoroughly, and then to use these as
a basis to establish the other identities when necessary.
2z 3 2 2z 2 22z3 3 2
4z 12z 9
6x 3 6x 3
x 4 4 x x 4 x 4
6x 3
x 4
32x 1
x 4
x
x2 x2
25 x 5
x
x 5x 5 x2x 5
x 5x 5
122. f x 2 tan
Amplitude: 2
x
2
x x3 5x 2
x 5x 5
x1 x2 5x
x 5x 5
xx2 5x 1
x 2 25
Period:
Two consecutive vertical
asymptotes:
Key points: 1 2 , 2 , 0, 0, 1
2
2
−3
x 1, x 1
, 2 2
3
−1
−1
−2
−3
y
1 3
x