Trigonometry Examples

2 sin (x) - \sqrt{3} = 0

$2 \sin (x) - \sqrt{3} = 0$

Step 1

Add

\sqrt{3}

$\sqrt{3}$ to both sides of the equation.

2 sin (x) = \sqrt{3}

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

Step 2

Divide each term in

2 sin (x) = \sqrt{3}

$2 \sin (x) = \sqrt{3}$ by

2

$2$ and simplify.

Tap for more steps...

Step 2.1

Divide each term in

2 sin (x) = \sqrt{3}

$2 \sin (x) = \sqrt{3}$ by

2

$2$ .

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

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

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Cancel the common factor of

2

$2$ .

Tap for more steps...

Step 2.2.1.1

Cancel the common factor.

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

Step 2.2.1.2

Divide

$\sin (x)$ by

$1$ .

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

Step 3

Take the inverse sine of both sides of the equation to extract

$x$ from inside the sine.

$x = \arcsin (\frac{\sqrt{3}}{2})$

Step 4

Simplify the right side.

Tap for more steps...

Step 4.1

The exact value of

$\arcsin (\frac{\sqrt{3}}{2})$ is

$60$ .

$x = 60$

Step 5

The sine function is positive in the first and second quadrants. To find the second solution, subtract the reference angle from

$180$ to find the solution in the second quadrant.

$x = 180 - 60$

Step 6

Subtract

$60$ from

$180$ .

$x = 120$

Step 7

Find the period of

$\sin (x)$ .

Tap for more steps...

Step 7.1

The period of the function can be calculated using

$\frac{360}{| b |}$ .

$\frac{360}{| b |}$

Step 7.2

Replace

$b$ with

$1$ in the formula for period.

$\frac{360}{| 1 |}$

Step 7.3

The absolute value is the distance between a number and zero. The distance between

$0$ and

$1$ is

$1$ .

$\frac{360}{1}$

Step 7.4

Divide

$360$ by

$1$ .

$360$

Step 8

The period of the

$\sin (x)$ function is

$360$ so values will repeat every

$360$ degrees in both directions.

$x = 60 + 360 n, 120 + 360 n$ , for any integer

$n$