Question

Find the exact value of cos 4pi/3 in simplest form with a rational denominator?

Answer 1

The given expression is

`cos(4\pi)/(3)`

Since the angle is greater than pi, then it lies in the 3rd quadrant

Since in the 3rd quadrant the value of cosine is negative, then we will use the expression

`cos(4\pi)/(3)=cos(\pi+(\pi)/(3))=-cos(\pi)/(3)`

Since the value of cos(pi/3) = 1/2, then

`\begin{gathered} cos(\pi)/(3)=(1)/(2) \\ \\ cos(4\pi)/(3)=-cos(\pi)/(3)=-(1)/(2) \end{gathered}`

The answer is -1/2