What is #cos ( (5pi)/3)#?

1 Answer
Aug 13, 2017

#frac(1)(2)#

Explanation:

We have: #cos(frac(5 pi)(3))#

#= cos(frac(3 pi)(3) + frac(2 pi)(3))#

#= cos(pi + frac(2 pi)(3))#

Let's apply the compound angle formula of #cos(theta)#:

#= cos(pi) cos(frac(2 pi)(3)) - sin(pi) sin(frac(2 pi)(3))#

#= - 1 cdot cos(2 cdot frac(pi)(3)) - 0 cdot sin(frac(2 pi)(3))#

#= - cos(2 cdot frac(pi)(3))#

Let's apply the double angle formula of #cos(theta)#:

#= - (2 cos^(2)(frac(pi)(3)) - 1)#

#= - (2 cdot (frac(1)(2))^(2) - 1)#

#= - (2 cdot frac(1)(4) - 1)#

#= - (frac(1)(2) - 1)#

#= - (- frac(1)(2))#

#= frac(1)(2)#