AP Precalculus Unit 3

csc θ

1/sin θ

sec θ

1/cos θ

cot θ

1/tan θ

tan θ

sin θ/cos θ

cot θ is ALSO

cos θ/sin θ

cos (π/2 - θ)

sin θ

sin (π/2-θ)

cos θ

tan (π/2-θ)

cot θ

1st Pythagorean identity

cos²θ + sin²θ = 1

second Pythagorean identity (sec)

1 + tan²θ = sec²θ

second Pythagorean identity (csc)

cot²θ + 1 = csc²θ

to find second Pythagorean…

divide first Pythagorean by either cos²θ or sin²θ

even function

f(-θ) = f(θ)

odd function

f(-θ) = -f(θ)

sin θ is_ (even/odd)

odd

cos θ is __ (even/odd)

even

tan θ is __ (even/odd)

odd

cscθ is (even/odd)

odd

sec θ is (even/odd)

even

cot θ is (even/odd)

odd

sin (a+b) = (double angle)

2 sin θ cos θ

cos (a+b)= (double angle)

2 cos²θ-1

sin 2θ

2 sinθcosθ

cos 2θ

cos²θ-sin²θ

sec (x) has VA at x=

π/2, -π/2, 3π/2

cot(x) has VA at x=

-π, π, 2π, 0

csc (x) has VA at x=

-π, π, 2π, 0

θ=

arc length/radius

sin starts at __ on the graph

(0,0) on midline, goes up

range of sin and cos

[ -1, 1]

cos starts at __ on graph

(0, 1) at maximum

period of cos and sin is __ but period of tan is__

2π vs π

tan vertical asymptotes

cos θ = 0 (where θ= π/2 + πk)

range of inverse sin

[-π/2, π/2]

range of inverse cos

[0, π]

range of inverse tan

(-π/2, π/2)- open interval!