Trigonometry Examples

${(2 \cos (60) \cdot (2 \sin (60)))}^{3}$

Step 1

Simplify the expression.

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Step 1.1

Add parentheses.

${(2 (\cos (60) \cdot (2 \sin (60))))}^{3}$

Step 1.2

Reorder $\cos (60)$ and $2 \sin (60)$ .

${(2 (2 \sin (60) \cdot \cos (60)))}^{3}$

Step 2

Apply the sine double-angle identity.

${(2 \sin (2 \cdot 60))}^{3}$

Step 3

Multiply $2$ by $60$ .

${(2 \sin (120))}^{3}$

Step 4

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

${(2 \sin (60))}^{3}$

Step 5

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

${(2 \frac{\sqrt{3}}{2})}^{3}$

Step 6

Cancel the common factor of $2$ .

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Step 6.1

Cancel the common factor.

${(2 \frac{\sqrt{3}}{2})}^{3}$

Step 6.2

Rewrite the expression.

${\sqrt{3}}^{3}$

Step 7

Rewrite ${\sqrt{3}}^{3}$ as $\sqrt{3^{3}}$ .

$\sqrt{3^{3}}$

Step 8

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

$\sqrt{27}$

Step 9

Rewrite $27$ as $3^{2} \cdot 3$ .

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Step 9.1

Factor $9$ out of $27$ .

$\sqrt{9 (3)}$

Step 9.2

Rewrite $9$ as $3^{2}$ .

$\sqrt{3^{2} \cdot 3}$

Step 10

Pull terms out from under the radical.

$3 \sqrt{3}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt{3}$

Decimal Form:

$5.19615242 \dots$