Trigonometry Examples

$8 (\cos (\frac{3 π}{2}) + i \sin (\frac{3 π}{2}))$

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.

$8 (\cos (\frac{π}{2}) + i \sin (\frac{3 π}{2}))$

Step 1.2

The exact value of $\cos (\frac{π}{2})$ is $0$ .

$8 (0 + i \sin (\frac{3 π}{2}))$

Step 1.3

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.

$8 (0 + i (- \sin (\frac{π}{2})))$

Step 1.4

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

$8 (0 + i (- 1 \cdot 1))$

Step 1.5

Multiply $- 1$ by $1$ .

$8 (0 + i \cdot - 1)$

Step 1.6

Move $- 1$ to the left of $i$ .

$8 (0 - 1 \cdot i)$

Step 1.7

Rewrite $- 1 i$ as $- i$ .

$8 (0 - i)$

Step 2

Simplify the expression.

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Step 2.1

Subtract $i$ from $0$ .

$8 (- i)$

Step 2.2

Multiply $- 1$ by $8$ .

$- 8 i$