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

1 Answer
Dec 6, 2017

#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)#.