Question

Which of the following is equivalent to csc⁡(-112°)?
csc⁡(68°)
csc⁡(112°)
-csc⁡(68°)
-csc⁡(-112°)

Answer 1

answer : -csc⁡(68°)

csc(-112°) =?  

Angle -112 lies in third quadrant  

csc is negative in third quadrant  

So csc(-112) = -csc(112)

We know csc(112) lies in second quadrant

csc(112) can be written as $csc(\pi - 68)$ = csc(68)

csc(-112) = -csc(112)  = -$csc(\pi - 68)$= -csc(68)