Chapter 1

y/r

sin Θ

x/r

cos Θ

y/x

tan Θ

r/y

csc Θ

r/x

sec Θ

x/y

cot Θ

0°

sin=0, cos=1, tan=0

90°

sin=1, cos=0, tan=und.

180°

sin=0, cos=-1, tan=0

270°

sin=-1, cos=0, tan=und.

Q1

all functions positive

Q2

sin and csc positive, rest negative

Q3

tan and cot positive, rest negative

Q4

cos and sec positive, rest negative

between -1 and 1

range of sin and cos

any real number

range of tan and cot

either greater than 1 or less than -1

range of sec and csc

sin²θ + cos²θ = 1

pythagorean identity with sin and cos

tan²θ + 1 = sec²θ

pythagorean identity with tan and sec

1 + cot²θ = csc²θ

pythagorean identity with cot and csc

sinθ/cosθ = tanθ

quotient identity with sin, cos, and tan

cosθ/sinθ = cotθ

quotient identity with cos, sin, and cot