Asked by Matt

Evaluate the expression.

arcsin (-1/2)

Is there a rule I am missing? How do I know which quadrant the triangle belongs in? That is the only thing that is stopping me. Much help appreciated.
Answered by Reiny
where is the sine negative?
Isn't it in quadrants III and IV ?

The sine of which angle is 1/2 ?
Isn't it 30º or pi/6 radians

so arcsin (-1/2) is 210º or 330º
which would be 7pi/6 or 11pi/6 radians
Answered by Matt
Sorry, my mistake. It is arccos, not arcsin. Also, the negative in the book is exactly in the middle. The book just says evaluate the expression.
Answered by Reiny
first of all
-1/2 = 1/-2 = -(1/2)
it makes no difference where the negative sign is

just repeat my steps from above, except use the properties of Cosine

1. the cosine is negative in the 2nd and 3rd quadrants.
2. cos (60 degrees) = cos pi/3 = 1/2

(hint: one of the answers is 2pi/3)
Answered by Matt
But how do I know where cosine (or tangent and sine) are positive? I don't understand.

Thanks for the help, btw.
Answered by Reiny
It is called the CAST rule
this page explains it well

(Broken Link Removed)
Answered by Matt
It all makes sense now!!!! Thanks, haha.
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