Free Trigonometry Solver
with Step-by-Step AI
Solve trig equations, verify identities, and work with the unit circle — all solutions in every quadrant, explained clearly. Free.
- Trig equations & unit circle
- Inverse trig functions
- Trig identities & proofs
- Law of sines & cosines
Step 3 — Quadrants where sin(x)=½: QI and QII
x=π/6 and x=5π/6
Verify: sin(π/6)=0.5 ✓ sin(5π/6)=0.5 ✓
Final Answer: x=π/6 and x=5π/6
Ctrl+Enter to solve instantly
Step 3 — Quadrants where sin(x)=½: QI and QII
x=π/6 and x=5π/6
Verify: sin(π/6)=0.5 ✓ sin(5π/6)=0.5 ✓
Final Answer: x=π/6 and x=5π/6
From problem to solution in seconds
Enter your trig problem
Type a trig equation, identity, or triangle problem. Use sin(), cos(), tan() notation or click θ and π buttons.
AI identifies the approach
Determines whether to use the unit circle, inverse trig, law of sines/cosines, or identity manipulation.
Follow each trig step clearly
See which quadrants apply, how identities transform, and why solutions appear where they do.
What this trigonometry solver handles
What Is a Free Trigonometry Solver?
A trigonometry solver takes an equation, identity, or triangle problem involving sine, cosine, tangent, or their inverses and returns a complete step-by-step solution. MathGPT Free’s trig solver handles both algebraic trig problems and geometric ones like the law of cosines.
The unit circle is central to trigonometry, and most solvers just return the angle without explaining why that angle appears in multiple quadrants. This tool shows the reference angle, identifies which quadrants contain valid solutions, and lists all solutions in the given interval.
How the Trig Solver Works for Different Problem Types
Solving trig equations
Isolates the trig function, finds the reference angle via inverse function, then determines all solutions in the interval using the CAST rule — showing which functions are positive in each quadrant.
Verifying trig identities
Works from one side of the identity and transforms it step by step using known identities until it matches the other side.
Law of sines and cosines
Selects law of sines or law of cosines depending on the given information, then solves for the missing quantity.
Trigonometry Problems This Solver Handles
- Finding exact trig values using the unit circle
- Solving trig equations for all solutions in [0, 2π]
- Verifying and applying trig identities
- Inverse trig: arcsin, arccos, arctan
- Law of sines for ASA and AAS triangles
- Law of cosines for SAS and SSS triangles
- Double-angle and half-angle formulas
- Period, amplitude, and phase shift
Real results from real students
“I never understood why trig equations have two solutions. This showed me the quadrant logic for the first time.”
“Law of cosines problems were killing me. Clear explanation of when to use it vs law of sines.”
“Great for checking identity proofs before submitting. Saves time on homework.”
Common questions
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