ap pre-calculus polar functions and trigonometry

sin(a + b)

sin(a + b)

(sin a x cos b) + (sin b x cos a)

sin 2 x

2 sin x cos x

sin(a-b)

(sin a x cos b) - (sin b x cos a)

sin²x + cos²x

1

cos(2x) in terms of cosine

1

cos(2x) in terms of cosine

2cos²x -1

cos(2x) in terms of sine and cosine

cos²x - sin²x

cos(a+b)

(cos a x cos b) - (sin a x sin b)

cos (a-b)

(cos a x cos b) + (sin a x sin b)

a > b

dimpled cardioid

a < b

inner loop

a = b

heart shaped

radius in a + bi form

r = (a² + b²)^1/2

y-coordinate in terms of radius and sin

y = r • sin x

x-coordinate in terms of r and cosine

x = r • cos x

1/csc x

sin x

1/sinx

csc x

1/secx

cos x

1/cosx

sec x

since/cosx

tanx

cosx/sinx

cotx

1 + tan²x

sec²x

1 + cot²x

csc²x