Trigonometry Examples

$10 \sqrt{2} \cos (\frac{11 π}{6})$

Step 1

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

$10 \sqrt{2} \cos (\frac{π}{6})$

Step 2

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

$10 \sqrt{2} \frac{\sqrt{3}}{2}$

Step 3

Cancel the common factor of $2$ .

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Step 3.1

Factor $2$ out of $10 \sqrt{2}$ .

$2 (5 \sqrt{2}) \frac{\sqrt{3}}{2}$

Step 3.2

Cancel the common factor.

$2 (5 \sqrt{2}) \frac{\sqrt{3}}{2}$

Step 3.3

Rewrite the expression.

$5 \sqrt{2} \sqrt{3}$

Step 4

Combine using the product rule for radicals.

$5 \sqrt{3 \cdot 2}$

Step 5

Multiply $3$ by $2$ .

$5 \sqrt{6}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$5 \sqrt{6}$

Decimal Form:

$12.24744871 \dots$