Trigonometric Equation Solver
Basic Trigonometric Equation Solver sin x = m
Choose the function and enter m as a number or a radical. Solutions can be written in radians or degrees, and you can list the roots inside an interval.
The solver above handles the basic equations sin x = m, cos x = m, and tan x = m, writes the general solution, and lists the solutions in an interval.
Formulas used
sin x = sin α ⇔ x = α + k2π or x = π − α + k2π
cos x = cos α ⇔ x = ±α + k2π
tan x = tan α ⇔ x = α + kπ
- sin x = m and cos x = m have solutions only when −1 ≤ m ≤ 1.
- k is any integer.
Worked example
Solve sin x = 1/2:
x = π/6 + k2π or x = 5π/6 + k2π
Enter the same values in the calculator above to see every step of the solution.
How to use the calculator
- Choose the function, enter the value m, and optionally an interval.
- Press the calculate button. The result appears instantly.
- Read the step-by-step solution, rendered with KaTeX, to check your own work.