Question

An angle of measure $\frac{4\pi }{3}$ intersects the unit circle at point ($-1/2,- \frac{\sqrt{3} }{2}$). What is the exact value of tan($\frac{4\pi }{3}$)?
a. -1/2
b. $\sqrt{3$
c. $\frac{\sqrt{3} }{3}$
d. $-\frac{\sqrt{3} }{2}$

Answer 1

Answer:

  b.  √3

Step-by-step 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.