Solve -1/sin(frac{3pi{2})}=1/-1=-1

$$- \frac { 1 } { \sin ( \frac { 3 \pi } { 2 } ) } = \frac { 1 } { - 1 } = - 1$$

Verify

Solution Steps

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

$$-\frac{1}{-1}=\frac{1}{-1}\text{ and }\frac{1}{-1}=-1$$

Divide 1 by -1 to get -1.

$$-\left(-1\right)=\frac{1}{-1}\text{ and }\frac{1}{-1}=-1$$

The opposite of -1 is 1.

$$1=\frac{1}{-1}\text{ and }\frac{1}{-1}=-1$$

Divide 1 by -1 to get -1.

$$1=-1\text{ and }\frac{1}{-1}=-1$$

Compare 1 and -1.

$$\text{false}\text{ and }\frac{1}{-1}=-1$$

Divide 1 by -1 to get -1.

$$\text{false}\text{ and }-1=-1$$

Compare -1 and -1.

$$\text{false}\text{ and }\text{true}$$

The conjunction of \text{false} and \text{true} is \text{false}.

$$\text{false}$$