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# Trigonometric Equations Calculator

## Get detailed solutions to your math problems with our Trigonometric Equations step-by-step calculator. Practice your math skills and learn step by step with our math solver. Check out all of our online calculators here.

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###  Difficult Problems

1

Here, we show you a step-by-step solved example of trigonometric equations. This solution was automatically generated by our smart calculator:

$8\sin\left(x\right)=2+\frac{4}{\csc\left(x\right)}$
2

The reciprocal sine function is cosecant: $\frac{1}{\csc(x)}=\sin(x)$

$8\sin\left(x\right)=2+4\sin\left(x\right)$
3

Group the terms of the equation by moving the terms that have the variable $x$ to the left side, and those that do not have it to the right side

$8\sin\left(x\right)-4\sin\left(x\right)=2$
4

Combining like terms $8\sin\left(x\right)$ and $-4\sin\left(x\right)$

$4\sin\left(x\right)=2$
5

Divide both sides of the equation by $4$

$\sin\left(x\right)=\frac{2}{4}$
6

Divide $2$ by $4$

$\sin\left(x\right)=\frac{1}{2}$
7

The angles where the function $\sin\left(x\right)$ is $0$ are

$x=30^{\circ}+360^{\circ}n,\:x=150^{\circ}+360^{\circ}n$
8

The angles expressed in radians in the same order are equal to

$x=\frac{1}{6}\pi+2\pi n,\:x=\frac{5}{6}\pi+2\pi n\:,\:\:n\in\Z$

##  Final answer to the problem

$x=\frac{1}{6}\pi+2\pi n,\:x=\frac{5}{6}\pi+2\pi n\:,\:\:n\in\Z$

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