Trigonometry Examples

$10 (\cos (270) + i \sin (270))$

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. Make the expression negative because cosine is negative in the third quadrant.

$10 (- \cos (90) + i \sin (270))$

Step 1.2

The exact value of $\cos (90)$ is $0$ .

$10 (- 0 + i \sin (270))$

Step 1.3

Multiply $- 1$ by $0$ .

$10 (0 + i \sin (270))$

Step 1.4

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 third quadrant.

$10 (0 + i (- \sin (90)))$

Step 1.5

The exact value of $\sin (90)$ is $1$ .

$10 (0 + i (- 1 \cdot 1))$

Step 1.6

Multiply $- 1$ by $1$ .

$10 (0 + i \cdot - 1)$

Step 1.7

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

$10 (0 - 1 \cdot i)$

Step 1.8

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

$10 (0 - i)$

Step 2

Simplify the expression.

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Step 2.1

Subtract $i$ from $0$ .

$10 (- i)$

Step 2.2

Multiply $- 1$ by $10$ .

$- 10 i$