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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 solution of

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

is

$$\color{blue}{x = -\frac{ 3 \arctan\left( 0.4 \right) }{ 4 } + \frac{ 3 }{ 4 }\pi n}~~~\text{where}~~ n \in \mathbb Z$$

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Script name : trigonometric-equation-solver

Imputed values: 0 , 3 , -4/3 , 0.4 , ex , rad , 0 , 360 , R

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Trigonometric Equation Solver
show help ↓↓ examples ↓↓
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( $\cdot$ x ) =

 exact solutions (default) an approximate solutions
 find all solutions (default) ≤ x ≤
working...
examples
example 1:ex 1:

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

example 2:ex 2:

Find all solutions of the equation $\cos \left( \frac{3x}{2} \right) = -\frac{\sqrt{2}}{2}$. Express the results in degrees.

example 3:ex 3:

Find exact solutions of the equation $\tan \left( -\frac{4x}{3} \right) = 0.4$. Express the results in radians.

example 4:ex 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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