# trigonometry

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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 -

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 -

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 -

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 -

But how do I know where cosine (or tangent and sine) are positive? I don't understand.

Thanks for the help, btw.

• trigonometry -

It is called the CAST rule

• trigonometry -

It all makes sense now!!!! Thanks, haha.