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

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

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

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