Trigonometry Examples

$\sin (\frac{π}{4} + x)$

Step 1

Apply the sum of angles identity.

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

Step 2

Simplify each term.

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

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

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