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 domain of sin all θ domain of cos all θ domain of tan θ does not = π/2 + nπ domain of cot θ does not = nπ domain of sec θ does not = π/2 + nπ domain of csc θ does not = nπ range of sin |sin θ| ≤ 1 range of cos |cos θ| ≤ 1 range of tan all reals range of cot all reals range of sec |sec θ| ≥ 1 range of csc |csc θ| ≥ 1 domain of inverse sin -1 ≤ x ≤ 1 domain of inverse cos -1 ≤ x ≤ 1 domain of inverse tan all real x range of inverse sin -π/2 ≤ y ≤ π/2 range of inverse cos 0 ≤ y ≤ π range of inverse tan -π/2 < y < π/2 sine y/r cosine x/r tangent y/x cosecant r/y secant r/x cotangent x/y 30º π/6 (√3/2, 1/2) 45º π/4 (√2/2, √2/2) 60º π/3 (1/2, √3/2) 90º π/2 (0, 1) 120º 2π/3 (-1/2, √3/2) 135º 3π/4 (-√2/2, √2/2) 150º 5π/6 (-√3/2, 1/2) 180º π (-1, 0) 210º 7π/6 (-√3/2, -1/2) 225º 5π/4 (-√2/2, -√2/2) 240º 4π/3 (-1/2, -√3/2) 270º 3π/2 (0, -1) 300º 5π/3 (1/2, -√3/2) 315º 7π/4 (√2/2, -√2/2) 330º 11π/6 (√3/2, -1/2) 360º 2π (1, 0) Arc Length (for rads) s = rθ Arc Length (for degrees) s = θ/360º x 2πr/1 Area of a sector (for degrees) K = θ/360º x πr² Area of a sector (for rads) K = 1/2 r² θ Area of a sector (for arc length) K = 1/2 r s degrees to rads (degreeº) x π/180º rads to degrees (rad) x 180º/π reciprocal of csc x 1/sin x reciprocal of sec x 1/cos x reciprocal of cot x 1/tan x reciprocal of sin x 1/csc x reciprocal of cos x 1/sec x reciprocal of tan x 1/cot x Quotient of tan x sin x/cos x Quotient of cot x cos x/sin x cos (-x) = cos x sin (-x) = - sin x csc (-x) = -csc x tan (-x) = -tan x sec (-x) = sec x cot (-x) = -cot x Pythagorian and variations of sec²x 1 + tan²x = sec²x 1 = sec²x - tan²x Pythagorian and variations of csc²x 1 + cot²x = csc²x 1 = csc²x - cot²x Pythagorian and variations of sin²x 1 - cos²x = sin²x 1 = sin²x + cos²x Pythagorian and variations of cos²x 1 - sin²x = cos²x sin²x - 1 = -cos²x 1 = sin²x + cos²x Cofunction of sin x cos (90º - θ) Cofunction of tan x cot (90º - θ) Cofunction of sec x csc (90º - θ)