Question

Write the expression as either the sine, cosine, or tangent of a single angle.

cos(pi/3)cos(pi/5)+sin(pi/3)sin(pi/5)

Answer 1

I think it probably has to do with the unit circle but I really have no idea what to do for it, so an explanation would be nice also :s

Answer 2

We know that:
\[cos(a\pm b)=cos(a)cos(b)\mp sin(a)sin(b)\]
So therefore:
\[cos(a)cos(b)+sin(a)sin(b)=cos(a-b)\]
So therefore:
\[cos\left(\frac{\pi}{3}\right)cos\left(\frac{\pi}{5}\right)+sin\left(\frac{\pi}{3}\right)sin\left(\frac{\pi}{5}\right)=cos\left(\frac{\pi}{3}-\frac{\pi}{5}\right)=cos\left(\frac{2\pi}{15}\right)\]

Answer 3

How do we know the first part? Is there an identity

Answer 4

I understand it now, thanks

Answer 5

Oh lol yeah the first is a identity lol

Answer 6

http://www.youtube.com/watch?v=zcEMKv5yIYs