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Trigonometry

Trigonometric equations, identities, and graphs

Our AI Trigonometry Solver is a free online trigonometry calculator that covers sin/cos/tan evaluations, inverse trig functions, trigonometric identities, and trig equations. Type any trig expression or upload a photo of a problem — the AI returns step-by-step solutions, unit-circle reasoning, automatic degree/radian conversion, and picks the right identity (Pythagorean, sum/difference, double-angle, half-angle) to simplify the work. Built for high-school trig, SAT/ACT prep, and precalculus-to-calculus transitions — no signup required. Pick a specific topic below to launch its dedicated trig solver.

Inverse Trigonometry Calculator

Evaluate arcsin, arccos, and arctan with step-by-step solutions

Sin Cos Tan Calculator

Evaluate and graph sine, cosine, and tangent functions with step-by-step explanations

Trigonometry Calculator

Solve trigonometric equations and evaluate trig functions with step-by-step solutions

Common trig values

Tap any cell for the exact value, derivation, and unit-circle context.

Sin

Sin(0°)

= 0

Sin(15°)

= (√6 − √2)/4

Sin(30°)

= 1/2

Sin(45°)

= √2/2

Sin(60°)

= √3/2

Sin(75°)

= (√6 + √2)/4

Sin(90°)

= 1

Sin(105°)

= (√6 + √2)/4

Sin(120°)

= √3/2

Sin(135°)

= √2/2

Sin(150°)

= 1/2

Sin(180°)

= 0

Sin(270°)

= -1

Sin(360°)

= 0
Cos

Cos(0°)

= 1

Cos(15°)

= (√6 + √2)/4

Cos(30°)

= √3/2

Cos(45°)

= √2/2

Cos(60°)

= 1/2

Cos(75°)

= (√6 − √2)/4

Cos(90°)

= 0

Cos(105°)

= (√2 − √6)/4

Cos(120°)

= -1/2

Cos(135°)

= -√2/2

Cos(150°)

= -√3/2

Cos(180°)

= -1

Cos(270°)

= 0

Cos(360°)

= 1
Tan

Tan(0°)

= 0

Tan(15°)

= 2 − √3

Tan(30°)

= √3/3

Tan(45°)

= 1

Tan(60°)

= √3

Tan(75°)

= 2 + √3

Tan(90°)

= undefined

Tan(105°)

= −(2 + √3)

Tan(120°)

= -√3

Tan(135°)

= -1

Tan(150°)

= -√3/3

Tan(180°)

= 0

Tan(270°)

= undefined

Tan(360°)

= 0

Frequently asked questions

What is an AI trigonometry solver?

An AI trigonometry solver is an online calculator that uses a large-language-model math engine to read a trig problem and return a step-by-step solution. AI-Math accepts typed input or photo uploads and handles sin/cos/tan evaluations, inverse trig, identity simplifications, and trig equations — automatically choosing the right identity and unit (degrees or radians).

Is the AI Trigonometry Solver free to use?

Yes. The AI Trigonometry Solver is free with no signup required. You can solve sin/cos/tan problems, simplify identities, and solve trig equations directly from any browser, including mobile.

Can it solve sin, cos, and tan problems step by step?

Yes. The Sin Cos Tan Calculator evaluates ratios for any angle (degrees or radians), shows the unit-circle reference angle, lists the relevant SOH-CAH-TOA setup for right triangles, and breaks the work into numbered steps you can follow.

Does it handle trigonometric identities like Pythagorean, double-angle, and half-angle?

Yes. The solver recognises Pythagorean, sum/difference, double-angle, half-angle, and product-to-sum identities, then applies the one that collapses the expression fastest. Each substitution is shown in its own step so you can verify the chain.

Can I solve trig equations like sin(x) = 1/2 with all solutions in a given range?

Yes. The Trigonometry Calculator solves equations such as sin(x) = 1/2, 2cos²(x) − 1 = 0, or tan(2x) = √3 over a specified interval (for example 0 ≤ x < 2π) and returns every solution along with the general-form expression (x = π/6 + 2πk, etc.).

Can I upload a photo of my trigonometry homework?

Yes. Tap the camera icon on any AI-Math solver, snap the textbook problem, and the OCR engine converts it to LaTeX before the AI solves it. This works for handwritten and printed problems including triangles diagrams with labelled sides and angles.