If I have 10sin pi/6 cos pi/6 and need to move it to a sum. I am using 1/2[sin(u+v)+sin(u-v)], do I put the "10" in front of both sin? ex.
1/2[10sin(u+v)+10sin(u-v)]??
well yes..
$\displaystyle A\sin\alpha\cos\beta = A\left(\frac{1}{2}\left[\sin(\alpha+\beta) + \sin(\alpha+\beta)\right]\right) = \left(\frac{1}{2}\left[A\sin(\alpha+\beta) + A\sin(\alpha+\beta)\right]\right)$
since you can distribute it..
but i noticed that the angles for cos and sin is the same..
you can just use $\displaystyle \sin (2A) = 2\sin A\cos A$
Hello, dashreeve!
You're doing fancy Trig and you can't do simple algebra?
I have .$\displaystyle 10\sin\frac{\pi}{6}\cos\frac{\pi}{6}$ .and need to move it to a sum.
I am using: $\displaystyle \sin u\cos v \;=\;\frac{1}{2}\bigg[\sin(u+v)+\sin(u-v)\bigg]$
Do I put the "10" in front of both sin?
. . $\displaystyle \frac{1}{2}\bigg[10\sin(u+v)+10\sin(u-v)\bigg]$
We have: .$\displaystyle 10\cdot\underbrace{\sin(u)\cos(v)}$ . . . Leave the 10 "out front" !!
. . $\displaystyle 10\cdot\overbrace{ \left(\frac{1}{2}\bigg[\sin(u + v) + \sin(u-v)\bigg]\right)} $ . . . . Got it?
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By the way . . . $\displaystyle 10\sin\frac{\pi}{6}\cos\frac{\pi}{6} \;=\;5\,\left(2\sin\frac{\pi}{6}\cos\frac{\pi}{6}\ right) \;=\;5\sin\frac{\pi}{3}$