Expand Using Sum/Difference Formulas sin(pi/4+x)

$\sin (\frac{π}{4} + x)$

Use the sum formula for sine to simplify the expression. The formula states that $\sin (A + B) = \sin (A) \cos (B) + \cos (A) \sin (B)$ .

$\sin (\frac{π}{4}) \cos (x) + \cos (\frac{π}{4}) \sin (x)$

Remove parentheses.

$\sin (\frac{π}{4}) \cos (x) + \cos (\frac{π}{4}) \sin (x)$

Simplify each term.

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

$\frac{\sqrt{2}}{2} \cos (x) + \cos (\frac{π}{4}) \sin (x)$

Combine $\frac{\sqrt{2}}{2}$ and $\cos (x)$ .

$\frac{\sqrt{2} \cos (x)}{2} + \cos (\frac{π}{4}) \sin (x)$

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

$\frac{\sqrt{2} \cos (x)}{2} + \frac{\sqrt{2}}{2} \sin (x)$

Combine $\frac{\sqrt{2}}{2}$ and $\sin (x)$ .

$\frac{\sqrt{2} \cos (x)}{2} + \frac{\sqrt{2} \sin (x)}{2}$

Simplify.

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Combine the numerators over the common denominator.

$\frac{\sqrt{2} \cos (x) + \sqrt{2} \sin (x)}{2}$

Factor $\sqrt{2}$ out of $\sqrt{2} \cos (x) + \sqrt{2} \sin (x)$ .

$\frac{\sqrt{2} (\cos (x) + \sin (x))}{2}$

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Name

Name	one billion six hundred ninety-seven million ninety-one thousand seven hundred ninety

Interesting facts

1697091790 has 16 divisors, whose sum is 3066656112
The reverse of 1697091790 is 0971907961
Previous prime number is 257

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 49
Digital Root 4

Name

Name	one billion one hundred thirty-three million seven hundred two thousand two hundred forty-six

Interesting facts

1133702246 has 16 divisors, whose sum is 1775340288
The reverse of 1133702246 is 6422073311
Previous prime number is 2711

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 29
Digital Root 2

Name

Name	forty million eight thousand three hundred eighty-one

Interesting facts

40008381 has 8 divisors, whose sum is 60965184
The reverse of 40008381 is 18380004
Previous prime number is 7

Basic properties

Is Prime? no
Number parity odd
Number length 8
Sum of Digits 24
Digital Root 6

Find the Reference Angle 220

Convert Degrees, Minutes, Seconds to Decimal Degrees 19 degrees 19'

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Graph (5x)/170=79y*(47(4))