Find the Reference Angle sin(-330 degrees )

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Trigonometry

$\sin (- 330 °)$

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

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

Apply the sine half-angle identity.

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

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

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

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

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

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

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

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

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

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

Combine the numerators over the common denominator.

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

Subtract $1$ from $2$ .

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

Multiply the numerator by the reciprocal of the denominator.

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

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

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

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

Multiply $2$ by $2$ .

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

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

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

Any root of $1$ is $1$ .

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

Simplify the denominator.

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

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

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

$\frac{1}{2}$

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2}$

Decimal Form:

$0.5$

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Name

Name	one billion six hundred fifty-nine million forty-one thousand two hundred ninety-two

Interesting facts

1659041292 has 32 divisors, whose sum is 4982572800
The reverse of 1659041292 is 2921409561
Previous prime number is 919

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 39
Digital Root 3

Name

Name	one billion six hundred sixty-eight million seventy-two thousand seven hundred twenty-six

Interesting facts

1668072726 has 16 divisors, whose sum is 2792375280
The reverse of 1668072726 is 6272708661
Previous prime number is 227

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 45
Digital Root 9

Name

Name	one billion five hundred fifty-four million eight hundred sixty-three thousand ninety-two

Interesting facts

1554863092 has 8 divisors, whose sum is 3498441966
The reverse of 1554863092 is 2903684551
Previous prime number is 2

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 43
Digital Root 7

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