Trigonometry Equations

Sine(θ) =

opp/hyp

Cosecant(θ) =

hyp/opp

Cosine(θ) =

adj/hyp

Secant(θ) =

hyp/adj

Tangent(θ) =

opp/adj

Cotangent(θ) =

adj/opp

Reciprocal of sine

Cosecant

Reciprocal of cosine

Secant

Reciprocal of tangent

Cotangent

sinθ/cosθ =

tanθ

cosθ/sinθ =

cotθ

1 =

sin²θ+cos²θ

sin²θ+cos²θ =

1

tan²θ+1 =

sec²θ

cot²θ+1 =

csc²θ

Formula for linear speed

v = rw

Formula for angular speed

w = θ/t

1 revolution =

2pi radians

Cofunction of sine

Cosine

Cofunction of secant

Cosecant

Cofunction of tangent

Cotangent

cos(90-θ) =

sinθ

__ trig functions are positive in quadrant 1

All trig functions are positive

__ trig functions are positive in quadrant 2

Sine and it’s reciprocal (cosecant) are positive

__ trig functions are positive in quadrant 3

Tangent and it’s reciprocal (cotangent) are positive

__ trig functions are positive in quadrant 4

Cosine and it’s reciprocal (secant) are positive

Sin and cos repeat themselves every

360 degrees/2pi radians

Tangent repeats itself every

180 degrees/pi radians

Even functions

Cosine and secant

Odd functions

sine cosecant tangent cotangent

Area of a sector

A = 1/2r²(θ)

Arc length

S = rθ

Arc length and area MUST be calculated in

radians