Calculus Examples

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

Step 1

Combine $\sqrt{3}$ and $\frac{2 π}{3}$ .

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

Step 2

Move $2$ to the left of $\sqrt{3}$ .

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

Step 3

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

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

Step 4

The exact value of $\cos (\frac{π}{3})$ is $\frac{1}{2}$ .

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

Step 5

Cancel the common factor of $2$ .

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Step 5.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

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

Step 5.2

Cancel the common factor.

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

Step 5.3

Rewrite the expression.

$\frac{2 \sqrt{3} π}{3} - 1$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{2 \sqrt{3} π}{3} - 1$

Decimal Form:

$2.62759872 \dots$