Solve 1/3sin^260^circ

$$\frac { 1 } { 3 } \sin ^ { 2 } 60 ^ { \circ }$$

Evaluate

$$\frac{1}{4}=0.25$$

Solution Steps

Get the value of \sin(60) from trigonometric values table.

$$\frac{1}{3}\times \left(\frac{\sqrt{3}}{2}\right)^{2}$$

To raise \frac{\sqrt{3}}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{1}{3}\times \frac{\left(\sqrt{3}\right)^{2}}{2^{2}}$$

Multiply \frac{1}{3} times \frac{\left(\sqrt{3}\right)^{2}}{2^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(\sqrt{3}\right)^{2}}{3\times 2^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{3}{3\times 2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{3}{3\times 4}$$

Multiply 3 and 4 to get 12.

$$\frac{3}{12}$$

Reduce the fraction \frac{3}{12} to lowest terms by extracting and canceling out 3.

$$\frac{1}{4}$$