How do you calculate csc^-1(-5)?

1 Answer
Nov 23, 2015

theta~~348.46^@, 191.54^@

Explanation:

csc^-1(-5)

csctheta=-5

1/sintheta=-5

sintheta=-1/5

theta=sin^-1(-1/5)

theta~~-11.54^@ (348.46^@)

However, since the CAST rule states that cosecant is also negative in quadrant 3, there is a second answer:

theta=(360^@-348.46^@)+180^@
theta=11.54^@+180^@
theta~~191.54^@