Trig question

Question

A student solves the inverse sine function and gets 330 ° for an answer. Is it correct? Why or why not?

Answer 1

The inverse sine function has range [-π/2, π/2].  So, when you find the inverse sine of a number, you will never get 330°(or 11π/6 in radians).

 

Sin^-1(-1/2) = the angle between -π/2 and π/2 whose sine is -1/2

 

                = -30°(or -π/6 radians)

Answer 2

The student could be correct because for example if we had the following 

 

sin X = -0.5

 

then we would have two possible answers which would lie in the third quadrant and the fourth quadrant since sine is negative in those quadrants.

 

therefore , our answers in the above case would be 210 and 330 degrees which is the value given in the question.

 

so the student could   right when he got 330 as his answer.