Question

A unit circle is shown in the coordinate plane. An angle of 5pi/3 radians is also drawn on the unit circle. Using the diagram, determine the value of cos 5pi/3

Answer 1

1/2

Step-by-step explanation:

In the unit circle, the pair (x,y) is defined below:

`(x,y)=((1)/(2),-\frac{\sqrt[]{3}}{2})`

First, we find the value of r, the hypotenuse.

`\begin{gathered} r^2=x^2+y^2 \\ r^2=((1)/(2))^2+(-\frac{\sqrt[]{3}}{2})^2 \\ r^2=(1)/(4)+(3)/(4) \\ r^2=(4)/(4) \\ r^2=1 \\ r=1 \end{gathered}`

We then evaluate the value of cos 5pi/3​.

`\begin{gathered} \cos \theta=(x)/(r) \\ \text{Therefore:} \\ \cos (5\pi)/(3)=(1)/(2)/1 \\ \cos (5\pi)/(3)=(1)/(2) \end{gathered}`