Unit 7 MATH 1414/2412

All the identities and equations

cscθ (reciprocal)

1/sinθ

secθ (reciprocal)

1/cosθ

cotθ (reciprocal)

1/tanθ

sinθ (reciprocal)

1/cscθ

cosθ (reciprocal)

1/secθ

taxθ (reciprocal)

1/cotθ

tanθ (quotient)

sinθ/cosθ

cotθ (quotient)

cosθ/sinθ

sin²θ + cos²θ

1

tan²θ + 1

sec²θ

1 + cot²θ

csc²θ

sin(–θ)

–sinθ

tan(–θ)

–tanθ

cos(–θ)

cosθ

sin(u + v)

sin u cos v + cos u sin v

sin(u – v)

sin u cos v – cos u sin v

cos(u + v)

cos u cos v – sin u sin v

cos(u – v)

cos u cos v + sin u sin v

tan(u + v)

(tan u + tan v) / (1 – tan u tan v)

tan(u - v)

(tan u – tan v) / (1 + tan u tan v)

sin2θ

2 sinθ cosθ = sin2θ

cos2θ

cos²θ 0 sin²θ
1 – 2sin²θ
2cos²θ – 1

tan2θ

(2tanθ) / (1 – tan²θ)

cos²θ

(1 + cos2θ) / 2

sin²θ

(1 – cos2θ) / 2

tan²θ

(1 – cos2θ) / (1 + cos2θ)

sin^-1 x

Domain: –1 ≤ x ≤ 1
Range: –(π/2) ≤ y ≤ (π/2)

cos^-1x

Domain: –1 ≤ x ≤ 1
Range 0 ≤ y ≤ π

tan^-1x

Domain: –∞ < x < ∞
Range: –(π/2) < y < (π/2)