Trigonometry Examples

$2 \cos (30) - 5 \sin (30)$

Step 1

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

$2 \frac{\sqrt{3}}{2} - 5 \sin (30)$

Step 2

Cancel the common factor of $2$ .

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Step 2.1

Cancel the common factor.

$2 \frac{\sqrt{3}}{2} - 5 \sin (30)$

Step 2.2

Rewrite the expression.

$\sqrt{3} - 5 \sin (30)$

Step 3

The exact value of $\sin (30)$ is $\frac{1}{2}$ .

$\sqrt{3} - 5 (\frac{1}{2})$

Step 4

Combine $- 5$ and $\frac{1}{2}$ .

$\sqrt{3} + \frac{- 5}{2}$

Step 5

Move the negative in front of the fraction.

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$- 0.76794919 \dots$