Trigonometry Examples

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

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

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))

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

Step 1.2

The exact value of

sin (60)

$\sin (60)$ is

\frac{\sqrt{3}}{2}

$\frac{\sqrt{3}}{2}$ .

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

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

Step 1.3

Combine

i

$i$ and

\frac{\sqrt{3}}{2}

$\frac{\sqrt{3}}{2}$ .

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

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

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

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