Sin(-120): how to find exact value with no calculator?

xxjct711xx

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May 23, 2006
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just to be positive...i have no way of knowing if my answers are right so how exactly would you go obout finding the exact answer for sin(-120) and no calculators
 
\(\displaystyle \L
\begin{array}{rcl}
\sin ( - x) & = & - \sin (x) \\
\sin ( - 120) & = & - \sin (120) = - \sin (2 \cdot 60) \\
\sin (2\theta ) & = & 2\sin (\theta )\cos (\theta ) \\
\end{array}\)
 
-120 degrees is co-terminal with 240 degrees

\(\displaystyle sin(-120) = sin(240) = -\frac{\sqrt{3}}{2}\)

the unit circle ... learn it, live it, love it.

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