Calculus Examples

$z = 4 \cos (150) + i \sin (150)$

Step 1

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

$z = 4 (- \cos (30)) + i \sin (150)$

Step 2

The exact value of $\cos (30)$ is $\frac{\sqrt{3}}{2}$ .

$z = 4 (- \frac{\sqrt{3}}{2}) + i \sin (150)$

Step 3

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.1

Move the leading negative in $- \frac{\sqrt{3}}{2}$ into the numerator.

$z = 4 \frac{- \sqrt{3}}{2} + i \sin (150)$

Step 3.2

Factor $2$ out of $4$ .

$z = 2 (2) \frac{- \sqrt{3}}{2} + i \sin (150)$

Step 3.3

Cancel the common factor.

$z = 2 \cdot 2 \frac{- \sqrt{3}}{2} + i \sin (150)$

Step 3.4

Rewrite the expression.

$z = 2 (- \sqrt{3}) + i \sin (150)$

Step 4

Multiply $- 1$ by $2$ .

$z = - 2 \sqrt{3} + i \sin (150)$

Step 5

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

$z = - 2 \sqrt{3} + i \sin (30)$

Step 6

The exact value of $\sin (30)$ is $\frac{1}{2}$ .

$z = - 2 \sqrt{3} + i \frac{1}{2}$

Step 7

Combine $i$ and $\frac{1}{2}$ .

$z = - 2 \sqrt{3} + \frac{i}{2}$