Find cscx.

Question

cotx=-(9/4)

cosx is less than 0

Answer 1

Latika, just recognize that cscx=1/sinx. For cotx<0, angle x either has to be either in the second or fourth quadrant. Since cosx is less than 0, then angle x is in the second quadrant. Moreover, cotx=cosx/sinx=-9/4. To determine cscx, you need to find the hypotenuse of the triangle and take its ratio to 4 in which sinx is 4/hypotenuse.

 

Let r= hypotenuse of the triangle = √(9^2+4^2)=√(81+16)=√97

 

Hence, cscx=√97/4.