Question

What is the value of tan 0 in the unit circle below?

Answer 1

1 / sqrt(3)

Explanation:

tan(o) = sin(o) / cos(o)

sin(o) is the vertical distance from the x-axis. and that is in this basic circle the y-coordinate of the point.

cos(o) is the horizontal distance from the y-axis. that is the x-coordinate of the point.

so,

tan(o) = (1/2) / (sqrt(3)/2) = (2×1) / (2×sqrt(3)) = 1/sqrt(3)