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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

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

which are in range $0 ^\circ \leq x \leq 360 ^\circ$ are

$$x = \frac{ 1 }{ 6 }\pi~~,~~x = \frac{ 7 }{ 6 }\pi~~,~~x = \frac{ 1 }{ 3 }\pi~~\text{and}~~x = \frac{ 4 }{ 3 }\pi$$

## Report an Error !

Script name : trigonometric-equation-solver

Imputed values: 0 , 1 , 2 , r3/2 , ex , rad , interval , 0 , 360

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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 ≤
 radians (default) degrees

## Examples on how to use this calculator

Example 1:

Solve

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

Express the results in radians.

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

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

Express the results in radians.

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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