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)