Trig Formulas and Indentities

Basic Trigonometric Identities

sine-squared plus cosine-squared: This is one of the most fundamental identities and it states that for any angle θ, (sin θ)^2 + (cos θ)^2 = 1.
secant: The secant of an angle θ in a right triangle is 1/(cos θ). Sec θ is not defined if cos θ = 0.
cosecant: Similarly, the cosecant of an angle θ is 1/(sin θ). Cosec θ is not defined if sin θ = 0.
cotangent: This is the reciprocal of tangent, cot θ = 1/(tan θ). It represents the ratio of the adjacent side to the opposite side in a right triangle.

sine and cosine: These identities stem from the Pythagorean theorem and relate sine, cosine, and 1. (sin θ)^2 + (cos θ)^2 = 1.
tan and sec: Another important identity [(tan θ)^2 + 1 = (sec θ)^2] relates tan and sec.
cot and cosec: Similarly, (cot θ)^2 + 1 = (cosec θ)^2, relating cot and cosec.

cosine double angle: This formula gives the cosine of a double angle in terms of the original angle, and is especially important for simplifying certain kinds of trigonometric expressions. cos2 θ = 1 - 2sin^2 θ = 2cos^2 θ - 1.
sine double angle: Similarly, sin2 θ = 2sin θ cos θ.
tangent double angle: The tangent of a double angle is given by tan2 θ = 2tan θ / 1 - tan^2 θ.

cosine half angle formula: This is useful when you find yourself needing the cosine of half an angle in terms of the original angle. cos(θ/2) = ±√[(1 + cos θ)/2]
sine half angle formula: sin(θ/2) = ±√[(1 - cos θ)/2]
tangent half angle formula: tan(θ/2) = ±√[(1 - cos θ) / (1 + cos θ)]