Solve 245^circ+cos^230^circ

$$245 ^ { \circ } + \cos ^ { 2 } 30 ^ { \circ }$$

Evaluate

$$\frac{983}{4}=245.75$$

Solution Steps

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

$$245+\left(\frac{\sqrt{3}}{2}\right)^{2}$$

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

$$245+\frac{\left(\sqrt{3}\right)^{2}}{2^{2}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 245 times \frac{2^{2}}{2^{2}}.

$$\frac{245\times 2^{2}}{2^{2}}+\frac{\left(\sqrt{3}\right)^{2}}{2^{2}}$$

Since \frac{245\times 2^{2}}{2^{2}} and \frac{\left(\sqrt{3}\right)^{2}}{2^{2}} have the same denominator, add them by adding their numerators.

$$\frac{245\times 2^{2}+\left(\sqrt{3}\right)^{2}}{2^{2}}$$

The square of \sqrt{3} is 3.

$$245+\frac{3}{2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$245+\frac{3}{4}$$

Add 245 and \frac{3}{4} to get \frac{983}{4}.

$$\frac{983}{4}$$