AP Calculus BC: Series Tests, Trig Identities & Formulas

sin²θ + cos²θ =

1

1 + tan²θ =

sec²θ

1 + cot²θ =

csc²θ

sin(2x) =

2sinxcosx

cos(2x) =

cos²x - sin²x

2cos²x-1

1-2sin²x

tan(2x) =

(2tanx) / (1-tan²x)

sin²x =

(1/2)√(1-cos2x)

cos²x =

(1/2)√(1+cos2x)

The derivative of a parametric function is…?

(dy/dt) / (dx/dt)

The second derivative of a parametric function is…?

(d/dt [dy/dx]) / (dx/dt)

Formula for the Arc Length of a parametric function:

∫_a^b√[ x’(t)² + y’(t)² ] dt

The vector function r’(t) =

<x’(t), y’(t)>

The vector function ∫_a^br(t) dt =

< ∫_a^b x(t) dt, ∫_a^b y(t) dt >

The polar function r(θ) =

y(θ) = rsinθ & x(θ) = rcosθ

The derivative of a parametric function is…?

(dy/dθ) / (dx/dθ)

The formula for the area of a polar graph is…?

(1/2) ∫_α^β r(θ)² dθ

f_avg =

1/(b-a) *∫_a^b f(x) dx

Divergence Test

If the limit as n approaches ∞ of a_n ……………………….