Trigonometry Examples

$2 (\cos (60) + i \sin (60))$

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

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

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

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

Step 2

Simplify terms.

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Step 2.1

Apply the distributive property.

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

Step 2.2

Cancel the common factor of $2$ .

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Step 2.2.1

Cancel the common factor.

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

Step 2.2.2

Rewrite the expression.

$1 + 2 \frac{i \sqrt{3}}{2}$

$1 + 2 \frac{i \sqrt{3}}{2}$

Step 2.3

Cancel the common factor of $2$ .

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Step 2.3.1

Cancel the common factor.

$1 + 2 \frac{i \sqrt{3}}{2}$

Step 2.3.2

Rewrite the expression.

$1 + i \sqrt{3}$

$1 + i \sqrt{3}$

$1 + i \sqrt{3}$

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