Calculus Examples

$- \frac{π \sin (\frac{3 π}{4})}{4}$

Step 1

Simplify the numerator.

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Step 1.1

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

$- \frac{π \sin (\frac{π}{4})}{4}$

Step 1.2

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

$- \frac{π \frac{\sqrt{2}}{2}}{4}$

Step 2

Combine $π$ and $\frac{\sqrt{2}}{2}$ .

$- \frac{\frac{π \sqrt{2}}{2}}{4}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$- (\frac{π \sqrt{2}}{2} \cdot \frac{1}{4})$

Step 4

Multiply $\frac{π \sqrt{2}}{2} \cdot \frac{1}{4}$ .

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Step 4.1

Multiply $\frac{π \sqrt{2}}{2}$ by $\frac{1}{4}$ .

$- \frac{π \sqrt{2}}{2 \cdot 4}$

Step 4.2

Multiply $2$ by $4$ .

$- \frac{π \sqrt{2}}{8}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{π \sqrt{2}}{8}$

Decimal Form:

$- 0.55536036 \dots$