Algebra Examples

$\sin (\frac{5 π}{4}) \cos (- \frac{11 π}{6})$

Step 1

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because sine is negative in the third quadrant.

$- \sin (\frac{π}{4}) \cos (- \frac{11 π}{6})$

Step 2

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

$- \frac{\sqrt{2}}{2} \cos (- \frac{11 π}{6})$

Step 3

Add full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$- \frac{\sqrt{2}}{2} \cos (\frac{π}{6})$

Step 4

The exact value of $\cos (\frac{π}{6})$ is $\frac{\sqrt{3}}{2}$ .

$- \frac{\sqrt{2}}{2} \cdot \frac{\sqrt{3}}{2}$

Step 5

Multiply $- \frac{\sqrt{2}}{2} \cdot \frac{\sqrt{3}}{2}$ .

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Step 5.1

Multiply $\frac{\sqrt{3}}{2}$ by $\frac{\sqrt{2}}{2}$ .

$- \frac{\sqrt{3} \sqrt{2}}{2 \cdot 2}$

Step 5.2

Combine using the product rule for radicals.

$- \frac{\sqrt{3 \cdot 2}}{2 \cdot 2}$

Step 5.3

Multiply $3$ by $2$ .

$- \frac{\sqrt{6}}{2 \cdot 2}$

Step 5.4

Multiply $2$ by $2$ .

$- \frac{\sqrt{6}}{4}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \frac{\sqrt{6}}{4}$

Decimal Form:

$- 0.61237243 \dots$