For any nonquadrantal angle theta sin theta and csc theta wi

For any nonquadrantal angle theta, sin theta and csc theta will have the same sign. Explain why.

Solution

The cosecant (csc ) function can be written as

Csc (x)=1/sin (x)

As a result of this as long as sin (x) does not equal to 0 (can\'t happen if not quandrant angle)

The csc(x) and sin (x) must have same angle because 1 ,which is always positive, when divided by negative answers gives negative and when divided by positive number gives positive.Inother words if sin (x) is positive, csc (x) must also be positive and viceversa.