Basic Math Examples

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

Step 1

Factor $\frac{1}{2}$ out of each term.

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

Step 2

Multiply $2 (- \frac{π}{3})$ .

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Step 2.1

Multiply $- 1$ by $2$ .

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

Step 2.2

Combine $- 2$ and $\frac{π}{3}$ .

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

Step 3

Move the negative in front of the fraction.

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

Step 4

Add full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$\frac{1}{2} \cdot (\sin (\frac{4 π}{3}) + 2)$

Step 5

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

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

Step 6

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

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

Step 7

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.56698729 \dots$