Question

An angle of measure
`(4\pi )/(3)` intersects the unit circle at point (
`-1/2,- (√(3) )/(2)`). What is the exact value of tan(
`(4\pi )/(3)`)?

a. -1/2
b.
`\sqrt{3`
c.
`(√(3) )/(3)`
d.
`-(√(3) )/(2)`

Answer 1

b. √3

Explanation:

Given a point on the unit circle that represents the position of the terminal ray of an angle, the tangent of that angle is the ratio of the y-coordinate to the x-coordinate.

tan(4π/3) = y/x = (-√3/2)/(-1/2) = √3/1

tan(4π/3) = √3

_____

Additional comment

A calculator can confirm this for you.