Trigonometry Quiz 2: Chapter 3-4 (equivalent Identities)

Area of a Sector of a Circle

A=1/2 r^2 θ

Cosine X Graph

Domain: (-∞,∞) Range: [-1 , 1] Amplitude: 1 Period: 2π

Sine X Graph

Domain: (-∞,∞) Range: [-1 , 1] Amplitude: 1 Period: 2π

Secant X Graph

Domain: {x|x ≠ (2n + 1) π/2, where n is any integer} Range: ( -∞, -1 ] U [ 1 , ∞) Period: 2π

Tangent X Graph

Domain: {x|x ≠ (2n + 1) π/2, where n is any integer} Range: (-∞,∞) Period: π

Cosecant X Graph

Domain: {x|x ≠ nπ, where n is any integer} Range: ( -∞, -1 ] U [ 1 , ∞) Period: 2π

Cotangent X Graph

Domain: {x|x ≠ nπ, where n is any integer} Range: (-∞,∞) Period: π

Arc Length Formula

s = rθ

Circular Functions

sin s = y csc s = 1/y cos s = x sec s = 1/x tan s = y/x cot s = x/y

Reciprocal Identities

sin θ = 1/csc θ cos θ = 1/sec θ tan θ = 1/cot θ

Even/Odd Identities

sin(-θ) = - sin θ csc (-θ) = - csc θ cos(-θ) = cos θ sec (-θ) = sec θ tan (-θ) = - tan θ cot (-θ) = - cot θ

Pythagorean Identities

sin^2 θ + cos^2 θ =1 (sin^2 θ = 1 - cos^2 θ) (cos^2 θ = 1 - sin^2 θ) 1 + tan^2 θ =sec^2 θ 1 + cot^2 θ =csc^2 θ

Quotient Identities

tanθ = sinθ/cosθ cotθ = cosθ/sinθ