Posted by Matt on Tuesday, May 19, 2009 at 8:06pm.
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.

trigonometry  Reiny, Tuesday, May 19, 2009 at 8:09pm
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

trigonometry  Matt, Tuesday, May 19, 2009 at 9:14pm
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.

trigonometry  Reiny, Tuesday, May 19, 2009 at 9:38pm
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)

trigonometry  Matt, Tuesday, May 19, 2009 at 9:45pm
But how do I know where cosine (or tangent and sine) are positive? I don't understand.
Thanks for the help, btw.

trigonometry  Reiny, Tuesday, May 19, 2009 at 9:50pm
It is called the CAST rule
this page explains it well
(Broken Link Removed)

trigonometry  Matt, Tuesday, May 19, 2009 at 9:53pm
It all makes sense now!!!! Thanks, haha.
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