Trigonometry Examples

$\frac{10 \sin (45)}{\sin (30)}$

Step 1

Separate fractions.

$\frac{10}{1} \cdot \frac{\sin (45)}{\sin (30)}$

Step 2

Rewrite $\frac{\sin (45)}{\sin (30)}$ as a product.

$\frac{10}{1} (\sin (45) \frac{1}{\sin (30)})$

Step 3

Write $\sin (45)$ as a fraction with denominator $1$ .

$\frac{10}{1} (\frac{\sin (45)}{1} \cdot \frac{1}{\sin (30)})$

Step 4

Simplify.

Tap for more steps...

Step 4.1

Divide $\sin (45)$ by $1$ .

$\frac{10}{1} (\sin (45) \frac{1}{\sin (30)})$

Step 4.2

Convert from $\frac{1}{\sin (30)}$ to $\csc (30)$ .

$\frac{10}{1} (\sin (45) \csc (30))$

Step 5

Divide $10$ by $1$ .

$10 (\sin (45) \csc (30))$

Step 6

The exact value of $\sin (45)$ is $\frac{\sqrt{2}}{2}$ .

$10 (\frac{\sqrt{2}}{2} \csc (30))$

Step 7

The exact value of $\csc (30)$ is $2$ .

$10 (\frac{\sqrt{2}}{2} \cdot 2)$

Step 8

Cancel the common factor of $2$ .

Tap for more steps...

Step 8.1

Cancel the common factor.

$10 (\frac{\sqrt{2}}{2} \cdot 2)$

Step 8.2

Rewrite the expression.

$10 \sqrt{2}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$10 \sqrt{2}$

Decimal Form:

$14.14213562 \dots$