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

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Answer 1 · 2015-11-23T04:28:48

#theta~~348.46^@, 191.54^@#

#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^@#