Trigonometry2D

Trigonometric Equations - Theory & Concepts - Trigonometry Periodic Solutions

Methods for solving linear, quadratic, and multiple-angle trigonometric equations.

Solve $\sin(x) = c$ and see how periodic solutions map onto the coordinate wave and the unit circle.

Value (

c

)0.50

-1.00.01.0

x_{1}

-5.7596 rad~ -1.83π

x_{2}

-3.6652 rad~ -1.17π

x_{3}

0.5236 rad~ 0.17π

x_{4}

2.6180 rad~ 0.83π

Trigonometric functions are periodic. The equation

\sin(x) = c

has general solutions

x = \arcsin(c) + 2n\pi

and

x = \pi - \arcsin(c) + 2n\pi

where

n \in \mathbb{Z}

For $\sin(x) = c$ , the horizontal line at height $y = c$ intersects the circle at the solution angles.

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