Trigonometry Examples

$2 \sin (45 °) + 4 \cos (30 °)$

Step 1

The exact value of $\sin (45 °)$ is $\frac{\sqrt{2}}{2}$ .

$2 \frac{\sqrt{2}}{2} + 4 \cos (30 °)$

Step 2

Cancel the common factor of $2$ .

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Step 2.1

Cancel the common factor.

$2 \frac{\sqrt{2}}{2} + 4 \cos (30 °)$

Step 2.2

Rewrite the expression.

$\sqrt{2} + 4 \cos (30 °)$

Step 3

The exact value of $\cos (30 °)$ is $\frac{\sqrt{3}}{2}$ .

$\sqrt{2} + 4 \frac{\sqrt{3}}{2}$

Step 4

Cancel the common factor of $2$ .

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Step 4.1

Factor $2$ out of $4$ .

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

Step 4.2

Cancel the common factor.

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

Step 4.3

Rewrite the expression.

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$4.87831517 \dots$