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# I have a question about my trig homework?

Ok, so the question to my homework asks for the exact value of the expression WITHOUT using a calculator. Keep in mind this question has to do with inverse trig functions.

Expression: (sin^-1) (sin 3 pi/2)

My work:

(sin^-1) (sin 3 pi/2)

3 pi/2

*I glanced at my unit circle*

-1

However when I typed in "-1" in my online homework, it was considered wrong. So it gave me another try and I put 3 pi/2 as my answer. That was also incorrect and the homework told me that the correct answer is -pi/2

HOW?????

This is my face after seeing the right answer:

http://www.bing.com/images/search?q=jackie+chan+me...

Please explain how -pi/2 is correct and show your work

### 1 Answer

- PopeLv 77 years agoFavorite Answer
sin⁻¹[sin(3π/2)]

= sin⁻¹(-1)

= -π/2

sin(3π/2) = sin(-π/2) = -1

But 3π/2 is not on the range of sin⁻¹(x), while -π/2 is.