Trigonometric Functions & Identities

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Trigonometric Functions & Identities

Identities

cot θ^2 + 1 = csc^2 θ

tan θ^2 + 1 = sec^2 θ

sin θ^2 + cos^2 θ = 1

cot θ = 1/tan θ

sec θ = 1/cos θ

csc θ = 1/sin θ

cot θ = cos θ/sin θ

tan θ = sin θ/cos θ

Trigonometric Identities are formulas or proofs that are very useful whenever a trigonometric function (or expression) is seen in an equation. They can be utilized when trying to convert all variables of an equation to one or two kinds. For example, say you have a problem that asks you to proof that csc θ x tan θ equals sec θ. By using the formulas for tan θ and csc θ, you can find 1/cos θ = sec θ, successfully establishing your identity. Trigonometric Identities are not only useful in this method, but many more relating to the field of Trigonometry.

Functions

y = cot-1 x means x = cot y

Restrictions: - infinity ≤ x ≤ infinity, 0 ≤ y ≤ 3.14

y = csc-1 x means x = csc y

Restrictions: |x| ≥ 1, -3.14/2 ≤ y ≤ 3.14, y cannot equal 0

y = sec-1 x means x = sec y

Restrictions: |x| ≥ 1, 0 ≤ y ≤ 3.14, y cannot equal 3.14/2

y = tan-1 x means x = tan y

Restrictions: - infinity ≤ x ≤ infinity, -3.14/2 ≤ y ≤ 3.14/2

y = cos-1 x means x = cos y

Restrictions: -1 ≤ x ≤ 1, 0 ≤ y ≤ 3.14

y = sin-1 x means x = sin y

Restrictions: -1 ≤ x ≤ 1, -3.14/2 ≤ y ≤ 3.14/2

The Six Trigonometric Functions are used to compare the angles of a triangle to the length of it's sides. They are a fundamental part of studying trigonometry. In the context of Pre-Calculus, the following Formulas aid in proving identities and solving for values ranging from degrees to radians to values. These formulas are imperative to understanding and being able to solve, as well as graph, trigonometric expressions.