Trigonometry Examples

$z = 5 (\cos (120 + i \sin (120)))$

Step 1

Simplify each term.

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Step 1.1

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

$z = 5 \cos (120 + i \sin (60))$

Step 1.2

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

$z = 5 \cos (120 + i \frac{\sqrt{3}}{2})$

Step 1.3

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

$z = 5 \cos (120 + \frac{i \sqrt{3}}{2})$