Solve cos(3pi/2)left(3pi/2+1right)+sin(3pi/2)

$$\cos ( \frac{ 3 \pi }{ 2 } ) \left( \frac{ 3 \pi }{ 2 } +1 \right) + \sin ( \frac{ 3 \pi }{ 2 } )$$

Evaluate

$$-1$$

Solution Steps

Get the value of \cos(\frac{3\pi }{2}) from trigonometric values table.

$$0\left(\frac{3\pi }{2}+1\right)+\sin(\frac{3\pi }{2})$$

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

$$0\left(\frac{3\pi }{2}+\frac{2}{2}\right)+\sin(\frac{3\pi }{2})$$

Since \frac{3\pi }{2} and \frac{2}{2} have the same denominator, add them by adding their numerators.

$$0\times \frac{3\pi +2}{2}+\sin(\frac{3\pi }{2})$$

Cancel out 2, the greatest common factor in 0 and 2.

$$0\left(3\pi +2\right)+\sin(\frac{3\pi }{2})$$

Get the value of \sin(\frac{3\pi }{2}) from trigonometric values table.

$$0\left(3\pi +2\right)-1$$

Use the distributive property to multiply 0 by 3\pi +2.

$$2\times 0-1$$

Multiply 2 and 0 to get 0.

$$0-1$$

Subtract 1 from 0 to get -1.

$$-1$$

Factor

$$-1$$