Trigonometry Examples

$\frac{\sin (45)}{\frac{\sin (30)}{20}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\sin (45) \frac{20}{\sin (30)}$

Step 2

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

$\frac{\sqrt{2}}{2} \cdot \frac{20}{\sin (30)}$

Step 3

Cancel the common factor of $2$ .

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Step 3.1

Factor $2$ out of $20$ .

$\frac{\sqrt{2}}{2} \cdot \frac{2 (10)}{\sin (30)}$

Step 3.2

Cancel the common factor.

$\frac{\sqrt{2}}{2} \cdot \frac{2 \cdot 10}{\sin (30)}$

Step 3.3

Rewrite the expression.

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

Step 4

Combine $\sqrt{2}$ and $\frac{10}{\sin (30)}$ .

$\frac{\sqrt{2} \cdot 10}{\sin (30)}$

Step 5

Move $10$ to the left of $\sqrt{2}$ .

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

Step 6

The exact value of $\sin (30)$ is $\frac{1}{2}$ .

$\frac{10 \sqrt{2}}{\frac{1}{2}}$

Step 7

Multiply the numerator by the reciprocal of the denominator.

$10 \sqrt{2} \cdot 2$

Step 8

Multiply $2$ by $10$ .

$20 \sqrt{2}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$20 \sqrt{2}$

Decimal Form:

$28.28427124 \dots$