Question

How do you use the unit circle to find the value of the trigonometric function tan pi/6?

Answer 1

`tan(pi/6)=sqrt(3)/3`

Explanation:

The point associated with `pi/6` on the unit circle is `(sqrt(3)/2,1/2)`. All points on the unit circle are of the form `(cos(theta),sin(theta))`.

By the ratio identity `tan(theta)=sin(theta)/cos(theta)`, so

`tan(pi/6)=sin(pi/6)/cos(pi/6)=(1/2)/(sqrt(3)/2)=1/sqrt(3)=sqrt(3)/3`.

If you're not supposed to use the ratio identity you could draw a triangle with `theta` the angle between the x-axis and the radius through `pi/6` and then use `tan(theta)=(opposite)/(adjacent)`.