Solve sin^2pi/4+1

$$\sin ^ { 2 } \frac { \pi } { 4 } + 1$$

Evaluate

$$\frac{3}{2}=1.5$$

Solution Steps

Get the value of \sin(\frac{\pi }{4}) from trigonometric values table.

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

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

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{2^{2}}{2^{2}}.

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

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

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

The square of \sqrt{2} is 2.

$$\frac{2}{2^{2}}+1$$

Calculate 2 to the power of 2 and get 4.

$$\frac{2}{4}+1$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{1}{2}+1$$

Add \frac{1}{2} and 1 to get \frac{3}{2}.

$$\frac{3}{2}$$

Factor

$$\frac{3}{2} = 1\frac{1}{2} = 1.5$$