Trigonometric identities are equations true for every angle. They are the toolbox for simplifying expressions, solving trig equations and integrating. Seeing them evaluated at a specific angle is a quick way to remember and check them.
How to use the Trig Identities Calculator
- Angle unit
- Angle θ
- Identity type
Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.
How it works
Pick the angle and a family of identities. The calculator evaluates both sides of each identity in that family at your angle.
Formula
sin²θ + cos²θ = 1, 1 + tan²θ = sec²θ, 1 + cot²θ = csc²θ
sin(−θ) = −sin θ, cos(θ + π/2) = −sin θ, sin 3θ = 3 sin θ − 4 sin³θ …
Worked example
Inputs — Angle unit: Degrees (°); Angle θ: 30; Identity type: Pythagorean.
Results — Identities at θ = sin²θ + cos²θ = 0.25 + 0.75 = 1
1 + tan²θ = sec²θ = 1.333333333
1 + cot²θ = csc²θ = 4; sin θ = 0.5; cos θ = 0.8660254038; tan θ = 0.5773502692.
Key terms
- Identity
- An equation true for all values of the variable.
Frequently asked questions
What is the most important trig identity?
sin²θ + cos²θ = 1, the Pythagorean identity.
Are identities the same as equations?
No – an identity holds for every angle, an equation only for some.
How do I prove an identity?
Transform one side into the other using known identities.
Which functions are odd?
Sine, tangent, cotangent and cosecant; cosine and secant are even.