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# Trigonometric equation solver

This calculator can solve basic trigonometric equations such as: $\color{blue}{ \sin(x) = \frac{1}{2} }$ or $\color{blue}{ \sqrt{2} \cos\left(-\frac{3x}{4}\right) - 1 = 0 }$.

The calculator will find exact or approximate solutions on custom range. Solution can be expressed either in radians or degrees.

Result

The solutions of

$$\cos\left( \frac{ 3 x}{ 2 } \right)=- \frac{\sqrt{ 2 }}{ 2 }$$

are

$$\color{blue}{x = 90^\circ + 240^\circ \cdot n}~~\text{and}~~\color{blue}{x = 150^\circ + 240^\circ \cdot n}~~~\text{where}~~ n \in \mathbb Z$$

## Report an Error !

Script name : trigonometric-equation-solver

Imputed values: 0 , 2 , 3/2 , -r2/2 , ex , deg , 0 , 360 , R

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## Share Result

Trigonometric Equation Solver
0 1 2 3 4 5 6 7 8 9 - / . del

( $\cdot$ x ) =

 exact solutions (default) an approximate solutions
 find all solutions (default) ≤ x ≤

## Examples on how to use this calculator

Example 1:

Solve

$$\sin(2x)=\frac{\sqrt{3}}{2} ~~ \text{for} ~~ 0 \leq x \leq 360^\circ$$

Example 2:

Find all solutions of the equation

$$\cos \left( \frac{3x}{2} \right) = -\frac{\sqrt{2}}{2}$$

Express the results in degrees.

Example 3:

Find exact solutions of the equation

$$\tan \left( -\frac{4x}{3} \right) = 0.4$$

Example 4:

Solve

$$2\sin \left( x \right) + \sqrt{2}= 0 ~~ \text{for} ~~ -180^\circ \leq x \leq 180^\circ$$

Express the results in degrees.

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