Trigonometry Examples

$\sin (\frac{π}{4} - B)$

Step 1

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

$\sin (\frac{π}{4}) \cos (B) - \cos (\frac{π}{4}) \sin (B)$

Step 2

Remove parentheses.

$\sin (\frac{π}{4}) \cos (B) - \cos (\frac{π}{4}) \sin (B)$

Step 3

Simplify each term.

Tap for more steps...

Step 3.1

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

$\frac{\sqrt{2}}{2} \cos (B) - \cos (\frac{π}{4}) \sin (B)$

Step 3.2

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

$\frac{\sqrt{2} \cos (B)}{2} - \cos (\frac{π}{4}) \sin (B)$

Step 3.3

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

$\frac{\sqrt{2} \cos (B)}{2} - \frac{\sqrt{2}}{2} \sin (B)$

Step 3.4

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

$\frac{\sqrt{2} \cos (B)}{2} - \frac{\sin (B) \sqrt{2}}{2}$

Step 4

Combine the numerators over the common denominator.

$\frac{\sqrt{2} \cos (B) - \sin (B) \sqrt{2}}{2}$