Trigonometry Equations

Trig Equation Solver

Solve sin(x) = k, cos(x) = k, tan(x) = k and special forms. Find all solutions in [0°, 360°) and the general solution with n·360° (or n·180° for tan). Graph shows intersections.

sin, cos, tan equations
All solutions in [0°, 360°)
General formula
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sin(x) = k
k value
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Solutions
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Solutions in [0°, 360°)
General Solution
Reference Angle
Step-by-Step Solution
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Graph — trig function with horizontal line y = k
Solving Trig Equations
sin(x) = k → ref = arcsin(|k|); x₁ = ref, x₂ = 180°−ref (Q I/II if k>0) cos(x) = k → ref = arccos(|k|); x₁ = ref, x₂ = 360°−ref tan(x) = k → ref = arctan(|k|); x₁ = ref or ref+180°

The key steps: (1) find the reference angle using the inverse function, (2) determine which quadrants satisfy the sign of k, (3) list all solutions in [0°, 360°), (4) write the general formula by adding n·360° (or n·180° for tan).

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