Trigonometry Examples

$10 (\cos (315 + i \sin (315)))$

Step 1

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because sine is negative in the fourth quadrant.

$10 \cos (315 + i (- \sin (45)))$

Step 2

The exact value of $\sin (45)$ is $\frac{\sqrt{2}}{2}$ .

$10 \cos (315 + i (- \frac{\sqrt{2}}{2}))$

Step 3

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

$10 \cos (315 - \frac{i \sqrt{2}}{2})$