Trigonometry Examples

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

Step 1

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

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Step 1.1

Apply the distributive property.

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

Step 1.2

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

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

Step 1.3

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

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

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$B \approx - 0.1, \frac{1}{5}, - 0.3, 0.3, - \frac{2}{5}, \frac{2}{5}, - \frac{1}{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$B \approx - 0.1, \frac{1}{5}, - 0.3, 0.3, - \frac{2}{5}, \frac{2}{5}, - \frac{1}{2}$

Decimal Form:

$B \approx - 0.1, 0.2, - 0.3, 0.3, - 0.4, 0.4, - 0.5$

Step 4