# Sine Law and Cosine Law

• Jun 2nd 2008, 03:50 PM
jays-9
Sine Law and Cosine Law
hey, I was just wondering when i would use sine law, opposed to cosine law and vice-versa.

Thanks!
• Jun 2nd 2008, 04:10 PM
Jonboy
You don't mean Law of Sines and Law of Cosines, right?

If you mean the law of sine, that is: $Sin\,\theta = \frac{opp}{hyp}$

And the law of cosine: $Cos\,\theta = \frac{adj}{hyp}$

Then you can use use either of them when you have a right triangle.

Which one depends on what you know, be it the opposite side, adjacent side, or the hypotenuse.
• Jun 2nd 2008, 07:18 PM
Chris L T521
Quote:

Originally Posted by jays-9
hey, I was just wondering when i would use sine law, opposed to cosine law and vice-versa.

Thanks!

You use the law of sines when you have two known angles and one known side in a triangle (AAS, ASA).

Law of Sines: $\frac{\sin(\alpha)}{A}=\frac{\sin(\beta)}{B}=\frac {\sin(\gamma)}{C}$

You use the law of cosines when you have two known sides and one known angle (triangle is SAS).

\begin{aligned}
\text{Law of Cosines: }&A^2=B^2+C^2-2BC\cos(\alpha) \\
&B^2=A^2+C^2-2AC\cos(\beta) \\
&C^2=A^2+B^2-2AB\cos(\gamma)
\end{aligned}