Trigonometry Examples

$2 (\cos (90) + i \sin (90)) \cdot (5 (\sin (60)))$

Step 1

Simplify each term.

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Step 1.1

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

$2 (0 + i \sin (90)) \cdot (5 (\sin (60)))$

Step 1.2

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

$2 (0 + i \cdot 1) \cdot (5 (\sin (60)))$

Step 1.3

Multiply $i$ by $1$ .

$2 (0 + i) \cdot (5 (\sin (60)))$

Step 2

Add $0$ and $i$ .

$2 i \cdot (5 (\sin (60)))$

Step 3

The exact value of $\sin (60)$ is $\frac{\sqrt{3}}{2}$ .

$2 i \cdot (5 \frac{\sqrt{3}}{2})$

Step 4

Combine $5$ and $\frac{\sqrt{3}}{2}$ .

$2 i \cdot \frac{5 \sqrt{3}}{2}$

Step 5

Cancel the common factor of $2$ .

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Step 5.1

Factor $2$ out of $2 i$ .

$2 (i) \cdot \frac{5 \sqrt{3}}{2}$

Step 5.2

Cancel the common factor.

$2 i \cdot \frac{5 \sqrt{3}}{2}$

Step 5.3

Rewrite the expression.

$i \cdot (5 \sqrt{3})$

Step 6

Move $5$ to the left of $i$ .

$5 i \sqrt{3}$