AP Precalc Unit 3 (yellow packet)

csc x

peaks at y=1 and y=-1 pi/2 and 3pi/2, NOT intersecting y-axis

sec x

peaks at y=1 and y=-1 and 0, pi, 2pi interSECting y-axis

cot x

slope down, inflection at pi/2 and 3pi/2 opposite of where tan inflection/asymptotes are

sin(x)csc(x)

1 (reciprocals)

cos(x)sec(x)

1 (reciprocals)

Double angle: sin(2x)

2sin(x)cos(x)

Double angle: cos(2x)

cos²(x)-sin²(x) / 2cos²(x)-1 / 1-2sin²(x)

Pythagorean: sin²x + cos²x

1

sin(A+B)

sinA cosB + cosA sinB

sin(A-B)

sinA cosB - cosA sinB

cos(A+B)

cosA cosB - sinA sinB

cos(A-B)

cosA cosB + sinA sinB

tan

sin/cos

cot

cos/sin

period =

2pi/B or pi/B

tan vert asymptotes

≠pi/2 + kpi where k is any integer

polar —> rectangular

x = r cos Ø, y = r sin Ø

rectangular —> polar

x² + y² = r² tanØ = y/x (x ≠ 0)

r pos/increasing

distance from origin increasing

r pos/decreasing

distance from origin decreasing

r neg/increasing

distance from origin decreasing

r neg/decreasing

distance from origin increasing

r = a cos(nØ)

n = odd petals

convex limacon (no loop)

a/b > 2

r = a sin(nØ)

n = even petals

limacon (w/ loop)

a/b < 1

cardioid (butt)

a/b = 1

Circles

radius a // cos, on right tangent to y-axis // sin, top tangent to x-axis

tan(π/6)

root3/3

tan(π/3)

root3