Convert from Radians to Degrees cos(pi/12)

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Trigonometry

$\cos (\frac{π}{12})$

To convert radians to degrees, multiply by $\frac{180}{π}$ , since a full circle is $360 °$ or $2 π$ radians.

$(\cos (\frac{π}{12})) \cdot \frac{180 °}{π}$

The exact value of $\cos (\frac{π}{12})$ is $\frac{\sqrt{6} + \sqrt{2}}{4}$ .

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Split $\frac{π}{12}$ into two angles where the values of the six trigonometric functions are known.

$\cos (\frac{π}{4} - \frac{π}{6}) \cdot \frac{180}{π}$

Apply the difference of angles identity $\cos (x - y) = \cos (x) \cos (y) + \sin (x) \sin (y)$ .

$(\cos (\frac{π}{4}) \cos (\frac{π}{6}) + \sin (\frac{π}{4}) \sin (\frac{π}{6})) \cdot \frac{180}{π}$

The exact value of $\cos (\frac{π}{4})$ is $\frac{\sqrt{2}}{2}$ .

$(\frac{\sqrt{2}}{2} \cos (\frac{π}{6}) + \sin (\frac{π}{4}) \sin (\frac{π}{6})) \cdot \frac{180}{π}$

The exact value of $\cos (\frac{π}{6})$ is $\frac{\sqrt{3}}{2}$ .

$(\frac{\sqrt{2}}{2} \cdot \frac{\sqrt{3}}{2} + \sin (\frac{π}{4}) \sin (\frac{π}{6})) \cdot \frac{180}{π}$

The exact value of $\sin (\frac{π}{4})$ is $\frac{\sqrt{2}}{2}$ .

$(\frac{\sqrt{2}}{2} \cdot \frac{\sqrt{3}}{2} + \frac{\sqrt{2}}{2} \sin (\frac{π}{6})) \cdot \frac{180}{π}$

The exact value of $\sin (\frac{π}{6})$ is $\frac{1}{2}$ .

$(\frac{\sqrt{2}}{2} \cdot \frac{\sqrt{3}}{2} + \frac{\sqrt{2}}{2} \cdot \frac{1}{2}) \cdot \frac{180}{π}$

Simplify $\frac{\sqrt{2}}{2} \cdot \frac{\sqrt{3}}{2} + \frac{\sqrt{2}}{2} \cdot \frac{1}{2}$ .

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Simplify each term.

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

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

$(\frac{\sqrt{2} \sqrt{3}}{2 \cdot 2} + \frac{\sqrt{2}}{2} \cdot \frac{1}{2}) \cdot \frac{180}{π}$

Combine using the product rule for radicals.

$(\frac{\sqrt{2 \cdot 3}}{2 \cdot 2} + \frac{\sqrt{2}}{2} \cdot \frac{1}{2}) \cdot \frac{180}{π}$

Multiply $2$ by $3$ .

$(\frac{\sqrt{6}}{2 \cdot 2} + \frac{\sqrt{2}}{2} \cdot \frac{1}{2}) \cdot \frac{180}{π}$

Multiply $2$ by $2$ .

$(\frac{\sqrt{6}}{4} + \frac{\sqrt{2}}{2} \cdot \frac{1}{2}) \cdot \frac{180}{π}$

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

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

$(\frac{\sqrt{6}}{4} + \frac{\sqrt{2}}{2 \cdot 2}) \cdot \frac{180}{π}$

Multiply $2$ by $2$ .

$(\frac{\sqrt{6}}{4} + \frac{\sqrt{2}}{4}) \cdot \frac{180}{π}$

Combine the numerators over the common denominator.

$\frac{\sqrt{6} + \sqrt{2}}{4} \cdot \frac{180}{π}$

Simplify terms.

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Cancel the common factor of $4$ .

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Factor $4$ out of $180$ .

$\frac{\sqrt{6} + \sqrt{2}}{4} \cdot \frac{4 (45)}{π}$

Cancel the common factor.

$\frac{\sqrt{6} + \sqrt{2}}{4} \cdot \frac{4 \cdot 45}{π}$

Rewrite the expression.

$(\sqrt{6} + \sqrt{2}) \cdot \frac{45}{π}$

Apply the distributive property.

$\sqrt{6} \frac{45}{π} + \sqrt{2} \frac{45}{π}$

Combine $\sqrt{6}$ and $\frac{45}{π}$ .

$\frac{\sqrt{6} \cdot 45}{π} + \sqrt{2} \frac{45}{π}$

Combine $\sqrt{2}$ and $\frac{45}{π}$ .

$\frac{\sqrt{6} \cdot 45}{π} + \frac{\sqrt{2} \cdot 45}{π}$

Simplify each term.

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Move $45$ to the left of $\sqrt{6}$ .

$\frac{45 \sqrt{6}}{π} + \frac{\sqrt{2} \cdot 45}{π}$

Move $45$ to the left of $\sqrt{2}$ .

$\frac{45 \sqrt{6}}{π} + \frac{45 \sqrt{2}}{π}$

$π$ is approximately equal to $3.14159265$ .

$\frac{45 \sqrt{6}}{3.14159265} + \frac{45 \sqrt{2}}{3.14159265}$

Convert to a decimal.

$55.34347316 °$

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Name

Name	three hundred fifty-seven million seven hundred seventy-nine thousand nine hundred twenty-five

Interesting facts

357779925 has 16 divisors, whose sum is 610611456
The reverse of 357779925 is 529977753
Previous prime number is 5

Basic properties

Is Prime? no
Number parity odd
Number length 9
Sum of Digits 54
Digital Root 9

Name

Name	thirty-nine million nine hundred forty-one thousand six hundred thirty-four

Interesting facts

39941634 has 16 divisors, whose sum is 81583488
The reverse of 39941634 is 43614993
Previous prime number is 47

Basic properties

Is Prime? no
Number parity even
Number length 8
Sum of Digits 39
Digital Root 3

Name

Name	one hundred ninety-nine million seven thousand three hundred ninety-seven

Interesting facts

199007397 has 16 divisors, whose sum is 227335680
The reverse of 199007397 is 793700991
Previous prime number is 233

Basic properties

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

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