Trigonometry Examples

${(5 i^{3})}^{3}$

Step 1

Factor out $i^{2}$ .

${(5 (i^{2} \cdot i))}^{3}$

Step 2

Rewrite $i^{2}$ as $- 1$ .

${(5 (- 1 \cdot i))}^{3}$

Step 3

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

${(5 (- i))}^{3}$

Step 4

Multiply $- 1$ by $5$ .

${(- 5 i)}^{3}$

Step 5

Apply the product rule to $- 5 i$ .

${(- 5)}^{3} i^{3}$

Step 6

Raise $- 5$ to the power of $3$ .

$- 125 i^{3}$

Step 7

Factor out $i^{2}$ .

$- 125 (i^{2} \cdot i)$

Step 8

Rewrite $i^{2}$ as $- 1$ .

$- 125 (- 1 \cdot i)$

Step 9

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

$- 125 (- i)$

Step 10

Multiply $- 1$ by $- 125$ .

$125 i$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$