Precalculus Examples

$6 \cdot \cos (\frac{7 π}{3}) + i \sin (\frac{7 π}{3})$

Step 1

Subtract full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$6 \cdot \cos (\frac{π}{3}) + i \sin (\frac{7 π}{3})$

Step 2

The exact value of $\cos (\frac{π}{3})$ is $\frac{1}{2}$ .

$6 \cdot \frac{1}{2} + i \sin (\frac{7 π}{3})$

Step 3

Cancel the common factor of $2$ .

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Step 3.1

Factor $2$ out of $6$ .

$2 (3) \cdot \frac{1}{2} + i \sin (\frac{7 π}{3})$

Step 3.2

Cancel the common factor.

$2 \cdot 3 \cdot \frac{1}{2} + i \sin (\frac{7 π}{3})$

Step 3.3

Rewrite the expression.

$3 + i \sin (\frac{7 π}{3})$

Step 4

Subtract full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$3 + i \sin (\frac{π}{3})$

Step 5

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

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

Step 6

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

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