Trigonometric Equation Solver Calculator

Work out trigonometric equation solver instantly with clear inputs, formula shown and shareable results.

About Trigonometric Equation Solver Calculator

Because the trig functions are periodic, every equation has infinitely many solutions. The inverse function gives the principal value, then the symmetry of each function generates the rest: sine repeats with 360° and is symmetric about 90°, cosine is even, and tangent repeats every 180°.

Formulas

sin x = k

x = arcsin k + 360°n or x = 180° − arcsin k + 360°n

cos x = k

x = ±arccos k + 360°n

tan x = k

x = arctan k + 180°n

Worked example

With the default values below, Trigonometric Equation Solver Calculator returns Principal solution of 30.0000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Equationone of sin x = k, cos x = k, tan x = k: sin x = k
Right-hand value k: 0.5

Results

Principal solution: 30.0000 °
Second solution in 0°–360°: 150.0000 °
General solution: x = 30° + 360°n or x = 150° + 360°n
Principal solution in radians: 0.52359878

Step by step

1Values used
2sin x = k
3cos x = k
4tan x = k
5Principal solution= 30.0000 °
6Second solution in 0°–360°= 150.0000 °
7General solution= x = 30° + 360°n or x = 150° + 360°n
8Principal solution in radians= 0.52359878

Assumptions and limits

The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

sin x = 0.5?

The principal solution is 30° and the second in one revolution is 150°.

Why does tan need only one family?

Its period is 180°, not 360°, so arctan k plus multiples of 180° already covers every solution.