Trigonometry Examples

$2 \sin (60) \cos (30)$

Step 1

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

$2 \frac{\sqrt{3}}{2} \cos (30)$

Step 2

Cancel the common factor of $2$ .

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Step 2.1

Cancel the common factor.

$2 \frac{\sqrt{3}}{2} \cos (30)$

Step 2.2

Rewrite the expression.

$\sqrt{3} \cos (30)$

Step 3

The exact value of $\cos (30)$ is $\frac{\sqrt{3}}{2}$ .

$\sqrt{3} \frac{\sqrt{3}}{2}$

Step 4

Multiply $\sqrt{3} \frac{\sqrt{3}}{2}$ .

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Step 4.1

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

$\frac{\sqrt{3} \sqrt{3}}{2}$

Step 4.2

Raise $\sqrt{3}$ to the power of $1$ .

$\frac{{\sqrt{3}}^{1} \sqrt{3}}{2}$

Step 4.3

Raise $\sqrt{3}$ to the power of $1$ .

$\frac{{\sqrt{3}}^{1} {\sqrt{3}}^{1}}{2}$

Step 4.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{{\sqrt{3}}^{1 + 1}}{2}$

Step 4.5

Add $1$ and $1$ .

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

Step 5

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

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Step 5.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$\frac{{(3^{\frac{1}{2}})}^{2}}{2}$

Step 5.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{3^{\frac{1}{2} \cdot 2}}{2}$

Step 5.3

Combine $\frac{1}{2}$ and $2$ .

$\frac{3^{\frac{2}{2}}}{2}$

Step 5.4

Cancel the common factor of $2$ .

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Step 5.4.1

Cancel the common factor.

$\frac{3^{\frac{2}{2}}}{2}$

Step 5.4.2

Rewrite the expression.

$\frac{3^{1}}{2}$

Step 5.5

Evaluate the exponent.

$\frac{3}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{2}$

Decimal Form:

$1.5$

Mixed Number Form:

$1 \frac{1}{2}$