Solve -3cos(pi/4)sin(pi/4)

$$-3 \cos ( \frac{ \pi }{ 4 } ) \sin ( \frac{ \pi }{ 4 } )$$

Evaluate

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

Solution Steps

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

$$-3\times \frac{\sqrt{2}}{2}\sin(\frac{\pi }{4})$$

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

$$-3\times \frac{\sqrt{2}}{2}\times \frac{\sqrt{2}}{2}$$

Multiply \frac{\sqrt{2}}{2} and \frac{\sqrt{2}}{2} to get \left(\frac{\sqrt{2}}{2}\right)^{2}.

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

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

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

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

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

The square of \sqrt{2} is 2.

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

Multiply -3 and 2 to get -6.

$$\frac{-6}{2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{-6}{4}$$

Reduce the fraction \frac{-6}{4} to lowest terms by extracting and canceling out 2.

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

Factor

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