Trigonometry Examples

$\sin (\frac{π}{3}) + 6 \cos (\frac{π}{4})$

Step 1

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

$\frac{\sqrt{3}}{2} + 6 \cos (\frac{π}{4})$

Step 2

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

$\frac{\sqrt{3}}{2} + 6 \frac{\sqrt{2}}{2}$

Step 3

Cancel the common factor of $2$ .

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Step 3.1

Factor $2$ out of $6$ .

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

Step 3.2

Cancel the common factor.

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

Step 3.3

Rewrite the expression.

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$5.10866609 \dots$