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

1 Answer
turksvids
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).

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