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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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Example

Solved Problems

Difficult Problems

1

Solved example of trigonometric equations

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

Move everything to the left hand side of the equation

$8\sin\left(x\right)-2-4\sin\left(x\right)=0$

4

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

$4\sin\left(x\right)-2=0$
5

Factor the polynomial $4\sin\left(x\right)-2$ by it's greatest common factor (GCF): $2$

$2\left(2\sin\left(x\right)-1\right)=0$

Divide both sides of the equation by $2$

$2\sin\left(x\right)-1=\frac{0}{2}$

Zero divided by anything is equal to zero

$2\sin\left(x\right)-1=0$
6

Divide both sides of the equation by $2$

$2\sin\left(x\right)-1=0$

We need to isolate the dependent variable , we can do that by simultaneously subtracting $-1$ from both sides of the equation

$2\sin\left(x\right)=0-1\cdot -1$

$x+0=x$, where $x$ is any expression

$2\sin\left(x\right)=-1\cdot -1$
7

We need to isolate the dependent variable , we can do that by simultaneously subtracting $-1$ from both sides of the equation

$2\sin\left(x\right)=-1\cdot -1$
8

Multiply $-1$ times $-1$

$2\sin\left(x\right)=1$

Divide both sides of the equation by $2$

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

Divide both sides of the equation by $2$

$2\sin\left(x\right)-1=\frac{0}{2}$

Zero divided by anything is equal to zero

$2\sin\left(x\right)-1=0$
9

Divide both sides of the equation by $2$

$\sin\left(x\right)=\frac{1}{2}$
10

Divide $1$ by $2$

$\sin\left(x\right)=\frac{1}{2}$
11

The angles where the function $\sin\left(x\right)$ is $\frac{1}{2}$ are

$x=30^{\circ}+360^{\circ}n,\:x=150^{\circ}+360^{\circ}n$
12

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

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

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