Finite Math Examples

${\sin (- 330)}^{o}$

Step 1

The exact value of $\sin (- 330)$ is $\frac{1}{2}$ .

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Step 1.1

Rewrite $- 330$ as an angle where the values of the six trigonometric functions are known divided by $2$ .

${\sin (\frac{- 660}{2})}^{o}$

Step 1.2

Apply the sine half-angle identity.

${(\pm \sqrt{\frac{1 - \cos (- 660)}{2}})}^{o}$

Step 1.3

Change the $\pm$ to $+$ because sine is positive in the first quadrant.

${\sqrt{\frac{1 - \cos (- 660)}{2}}}^{o}$

Step 1.4

Simplify $\sqrt{\frac{1 - \cos (- 660)}{2}}$ .

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Step 1.4.1

Add full rotations of $360$ ° until the angle is between $0$ ° and $360$ °.

${\sqrt{\frac{1 - \cos (60)}{2}}}^{o}$

Step 1.4.2

The exact value of $\cos (60)$ is $\frac{1}{2}$ .

${\sqrt{\frac{1 - \frac{1}{2}}{2}}}^{o}$

Step 1.4.3

Write $1$ as a fraction with a common denominator.

${\sqrt{\frac{\frac{2}{2} - \frac{1}{2}}{2}}}^{o}$

Step 1.4.4

Combine the numerators over the common denominator.

${\sqrt{\frac{\frac{2 - 1}{2}}{2}}}^{o}$

Step 1.4.5

Subtract $1$ from $2$ .

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

Step 1.4.6

Multiply the numerator by the reciprocal of the denominator.

${\sqrt{\frac{1}{2} \cdot \frac{1}{2}}}^{o}$

Step 1.4.7

Multiply $\frac{1}{2} \cdot \frac{1}{2}$ .

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Step 1.4.7.1

Multiply $\frac{1}{2}$ by $\frac{1}{2}$ .

${\sqrt{\frac{1}{2 \cdot 2}}}^{o}$

Step 1.4.7.2

Multiply $2$ by $2$ .

${\sqrt{\frac{1}{4}}}^{o}$

Step 1.4.8

Rewrite $\sqrt{\frac{1}{4}}$ as $\frac{\sqrt{1}}{\sqrt{4}}$ .

${(\frac{\sqrt{1}}{\sqrt{4}})}^{o}$

Step 1.4.9

Any root of $1$ is $1$ .

${(\frac{1}{\sqrt{4}})}^{o}$

Step 1.4.10

Simplify the denominator.

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Step 1.4.10.1

Rewrite $4$ as $2^{2}$ .

${(\frac{1}{\sqrt{2^{2}}})}^{o}$

Step 1.4.10.2

Pull terms out from under the radical, assuming positive real numbers.

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

Step 2

Apply the product rule to $\frac{1}{2}$ .

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

Step 3

One to any power is one.

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

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2 °}$

Decimal Form:

$0.5$