Trigonometry Solver

The Trigonometry Solver covers the trig unit end to end. Solve equations like 2 sin x - 1 = 0 on a given interval, returning every solution and the general solution. Verify identities by transforming one side to the other with the identity used at each step. Evaluate exact values from the unit circle. Solve right triangles and oblique triangles with the law of sines and the law of cosines, including the ambiguous SSA case. Convert between degrees and radians. Find amplitude, period, phase shift, and vertical shift of a sinusoid. Inverse trigonometric expressions, sum and difference formulas, double- and half-angle formulas, and product-to-sum conversions are applied with the formula written before the substitution.

Type the problem or photograph it. For an equation, include the interval: "on [0, 2pi)" or "for 0 to 360 degrees". For an identity, write both sides with the word "verify" or "prove". For a triangle, list the known sides and angles with their labels. Use sin(x), cos^2(x), tan(2x), arcsin, and pi. Set Answer form to exact for unit-circle values, decimal for calculator-style answers. For a graphing question, give the equation and the solver reports the five key points of one period along with the transformations from the parent function. For a bearing or angle-of-elevation word problem, paste the whole problem and the solver sketches the triangle in words before applying a ratio.

Output: the solution set, the completed identity, or the triangle's missing parts first. Then the working: the reference angle, the quadrants, the general solution, or the identity applied on each line, or the law used with the substitution shown. Ambiguous-case triangles show both candidate triangles. The working is shown so you can check it. For pure geometry without trig ratios, use the Geometry Solver. For a trig function's calculus, use the Derivative or Integral Calculator. A follow-up can convert the solutions between degrees and radians, extend them to a different interval, or show the identity verified from the other side. Reference angles and quadrant reasoning are written out, since that is where most sign errors happen.