Trigonometry Examples

$\sin (x + \frac{π}{4})$

Step 1

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

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

Step 2

Remove parentheses.

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

Step 3

Simplify each term.

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Step 3.1

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

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

Step 3.2

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

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

Step 3.3

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

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

Step 3.4

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

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

Step 4

Combine the numerators over the common denominator.

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