Question

cos 16pi/3

Answer 1

Are you looking for the numerical value of this?

Answer 2

If so, cos(16pi/3) = cos(15pi/3 + pi/3) so we can take this as just cos(pi/3) which is sqrt(3)/2

Answer 3

Gahh, sorry that was sin! This is 1/2

Answer 4

\(\cos\left(\dfrac{16\pi}{3}\right) = \cos\left(\dfrac{10\pi}{3}\right) = \cos\left(\dfrac{4\pi}{3}\right)\)

Answer 5

Thanks tkhunny but i would like to understand why

Answer 6

Great. You tell me. Why would those three things be the same? Think about the Period of the Cosine Function.

Answer 7

2pi but still dont get that

Answer 8

I said "think about", not just "tell me" what it is.

What is the difference between the first argument and the second argument?
What is the difference between the second argument and the third argument?

Answer 9

\(\begin{array}{llll}
\cfrac{16}{3}\implies& 5+\cfrac{1}{3}\implies & \bf 2+2+1+\cfrac{1}{3}\\ \quad \\
\cfrac{16\pi}{3}\implies& 5\pi+\cfrac{\pi}{3}\implies& \bf2\pi+2\pi+\pi+\cfrac{\pi}{3}
\end{array}\)