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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