Solve 22sin30+4sin^260

$$22 \sin 30 + 4 \sin ^ { 2 } 60$$

Evaluate

$$14$$

Solution Steps

Get the value of \sin(30) from trigonometric values table.

$$22\times \frac{1}{2}+4\left(\sin(60)\right)^{2}$$

Multiply 22 and \frac{1}{2} to get 11.

$$11+4\left(\sin(60)\right)^{2}$$

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

$$11+4\times \left(\frac{\sqrt{3}}{2}\right)^{2}$$

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

$$11+4\times \frac{\left(\sqrt{3}\right)^{2}}{2^{2}}$$

Express 4\times \frac{\left(\sqrt{3}\right)^{2}}{2^{2}} as a single fraction.

$$11+\frac{4\left(\sqrt{3}\right)^{2}}{2^{2}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 11 times \frac{2^{2}}{2^{2}}.

$$\frac{11\times 2^{2}}{2^{2}}+\frac{4\left(\sqrt{3}\right)^{2}}{2^{2}}$$

Since \frac{11\times 2^{2}}{2^{2}} and \frac{4\left(\sqrt{3}\right)^{2}}{2^{2}} have the same denominator, add them by adding their numerators.

$$\frac{11\times 2^{2}+4\left(\sqrt{3}\right)^{2}}{2^{2}}$$

The square of \sqrt{3} is 3.

$$11+\frac{4\times 3}{2^{2}}$$

Multiply 4 and 3 to get 12.

$$11+\frac{12}{2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$11+\frac{12}{4}$$

Divide 12 by 4 to get 3.

$$11+3$$

Add 11 and 3 to get 14.

$$14$$