Trigonometry Examples

$\frac{x}{\sin (60)} = \frac{5}{5}$

Step 1

Solve for $y$ .

Tap for more steps...

Step 1.1

Multiply both sides by $3$ .

$\frac{2 x \sqrt{3}}{3} \cdot 3 = 1 \cdot 3$

Step 1.2

Simplify.

Tap for more steps...

Step 1.2.1

Simplify the left side.

Tap for more steps...

Step 1.2.1.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 1.2.1.1.1

Cancel the common factor.

$\frac{2 x \sqrt{3}}{3} \cdot 3 = 1 \cdot 3$

Step 1.2.1.1.2

Rewrite the expression.

$2 x \sqrt{3} = 1 \cdot 3$

Step 1.2.2

Simplify the right side.

Tap for more steps...

Step 1.2.2.1

Multiply $3$ by $1$ .

$2 x \sqrt{3} = 3$

Step 1.3

Divide each term in $2 x \sqrt{3} = 3$ by $2 \sqrt{3}$ and simplify.

Tap for more steps...

Step 1.3.1

Divide each term in $2 x \sqrt{3} = 3$ by $2 \sqrt{3}$ .

$\frac{2 x \sqrt{3}}{2 \sqrt{3}} = \frac{3}{2 \sqrt{3}}$

Step 1.3.2

Simplify the left side.

Tap for more steps...

Step 1.3.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.3.2.1.1

Cancel the common factor.

$\frac{2 x \sqrt{3}}{2 \sqrt{3}} = \frac{3}{2 \sqrt{3}}$

Step 1.3.2.1.2

Rewrite the expression.

$\frac{x \sqrt{3}}{\sqrt{3}} = \frac{3}{2 \sqrt{3}}$

Step 1.3.2.2

Cancel the common factor of $\sqrt{3}$ .

Tap for more steps...

Step 1.3.2.2.1

Cancel the common factor.

$\frac{x \sqrt{3}}{\sqrt{3}} = \frac{3}{2 \sqrt{3}}$

Step 1.3.2.2.2

Divide $x$ by $1$ .

$x = \frac{3}{2 \sqrt{3}}$

Step 1.3.3

Simplify the right side.

Tap for more steps...

Step 1.3.3.1

Multiply $\frac{3}{2 \sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

$x = \frac{3}{2 \sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}}$

Step 1.3.3.2

Combine and simplify the denominator.

Tap for more steps...

Step 1.3.3.2.1

Multiply $\frac{3}{2 \sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

$x = \frac{3 \sqrt{3}}{2 \sqrt{3} \sqrt{3}}$

Step 1.3.3.2.2

Move $\sqrt{3}$ .

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

Step 1.3.3.2.3

Raise $\sqrt{3}$ to the power of $1$ .

$x = \frac{3 \sqrt{3}}{2 ({\sqrt{3}}^{1} \sqrt{3})}$

Step 1.3.3.2.4

Raise $\sqrt{3}$ to the power of $1$ .

$x = \frac{3 \sqrt{3}}{2 ({\sqrt{3}}^{1} {\sqrt{3}}^{1})}$

Step 1.3.3.2.5

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x = \frac{3 \sqrt{3}}{2 {\sqrt{3}}^{1 + 1}}$

Step 1.3.3.2.6

Add $1$ and $1$ .

$x = \frac{3 \sqrt{3}}{2 {\sqrt{3}}^{2}}$

Step 1.3.3.2.7

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

Tap for more steps...

Step 1.3.3.2.7.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$x = \frac{3 \sqrt{3}}{2 {(3^{\frac{1}{2}})}^{2}}$

Step 1.3.3.2.7.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x = \frac{3 \sqrt{3}}{2 \cdot 3^{\frac{1}{2} \cdot 2}}$

Step 1.3.3.2.7.3

Combine $\frac{1}{2}$ and $2$ .

$x = \frac{3 \sqrt{3}}{2 \cdot 3^{\frac{2}{2}}}$

Step 1.3.3.2.7.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.3.3.2.7.4.1

Cancel the common factor.

$x = \frac{3 \sqrt{3}}{2 \cdot 3^{\frac{2}{2}}}$

Step 1.3.3.2.7.4.2

Rewrite the expression.

$x = \frac{3 \sqrt{3}}{2 \cdot 3^{1}}$

Step 1.3.3.2.7.5

Evaluate the exponent.

$x = \frac{3 \sqrt{3}}{2 \cdot 3}$

Step 1.3.3.3

Cancel the common factor of $3$ .

Tap for more steps...

Step 1.3.3.3.1

Cancel the common factor.

$x = \frac{3 \sqrt{3}}{2 \cdot 3}$

Step 1.3.3.3.2

Rewrite the expression.

$x = \frac{\sqrt{3}}{2}$

Step 2

Since $x = \frac{\sqrt{3}}{2}$ is a vertical line, there is no y-intercept and the slope is undefined.

Slope: Undefined

y-intercept: No y-intercept

Step 3

Find two points on the line.

$\begin{array}{c} x & y \\ \frac{\sqrt{3}}{2} & 0 \\ \frac{\sqrt{3}}{2} & 1 \end{array}$

Step 4

Graph the line using the slope, y-intercept, and two points.

Slope: Undefined

y-intercept: No y-intercept

$\begin{array}{c} x & y \\ \frac{\sqrt{3}}{2} & 0 \\ \frac{\sqrt{3}}{2} & 1 \end{array}$

Step 5