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