Trigonometry Examples

$12 (\cos (60) + i \sin (60))$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

The exact value of $\cos (60)$ is $\frac{1}{2}$ .

$12 (\frac{1}{2} + i \sin (60))$

Step 1.2

The exact value of $\sin (60)$ is $\frac{\sqrt{3}}{2}$ .

$12 (\frac{1}{2} + i \frac{\sqrt{3}}{2})$

Step 1.3

Combine $i$ and $\frac{\sqrt{3}}{2}$ .

$12 (\frac{1}{2} + \frac{i \sqrt{3}}{2})$

$12 (\frac{1}{2} + \frac{i \sqrt{3}}{2})$

Step 2

Simplify terms.

Tap for more steps...

Step 2.1

Apply the distributive property.

$12 (\frac{1}{2}) + 12 \frac{i \sqrt{3}}{2}$

Step 2.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.2.1

Factor $2$ out of $12$ .

$2 (6) \frac{1}{2} + 12 \frac{i \sqrt{3}}{2}$

Step 2.2.2

Cancel the common factor.

$2 \cdot 6 \frac{1}{2} + 12 \frac{i \sqrt{3}}{2}$

Step 2.2.3

Rewrite the expression.

$6 + 12 \frac{i \sqrt{3}}{2}$

$6 + 12 \frac{i \sqrt{3}}{2}$

Step 2.3

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.3.1

Factor $2$ out of $12$ .

$6 + 2 (6) \frac{i \sqrt{3}}{2}$

Step 2.3.2

Cancel the common factor.

$6 + 2 \cdot 6 \frac{i \sqrt{3}}{2}$

Step 2.3.3

Rewrite the expression.

$6 + 6 (i \sqrt{3})$

$6 + 6 i \sqrt{3}$

$6 + 6 i \sqrt{3}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$