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Which of the following best explains why tangent StartFraction 5 pi Over 6 EndFraction not-equals tangent StartFraction 5 pi Over 3 EndFraction? The angles do not have the same reference angle. Tangent is positive in the second quadrant and negative in the fourth quadrant. Tangent is negative in the second quadrant and positive in the fourth quadrant. The angles do not have the same reference angle or the same sign.

Respuesta :

Using reference angles, it is found that the correct option is:

  • The angles do not have the same reference angle.

Angle [tex]\frac{5\pi}{6}[/tex] is on the second quadrant, [tex]\frac{\pi}{2} < \frac{5\pi}{6} < \pi[/tex].

  • On the second quadrant, the tangent is negative, as the sine is positive and the cosine is negative.
  • The reference angle is found subtracting [tex]\pi[/tex] from the angle, hence:

[tex]\pi - \frac{5\pi}{6} = \frac{6\pi}{6} - \frac{5\pi}{6} = \frac{\pi}{6}[/tex]

Angle [tex]\frac{5\pi}{3}[/tex] is on the fourth quadrant, [tex]\frac{3\pi}{2} < \frac{5\pi}{3} < 2\pi[/tex].

  • On the second quadrant, the tangent is negative, as the sine is negative and the cosine is positive.
  • The reference angle is found subtracting [tex]2\pi[/tex] from the angle, hence:

[tex]2\pi - \frac{5\pi}{3} = \frac{6\pi}{3} - \frac{5\pi}{3} = \frac{\pi}{3}[/tex]

They have different reference angles, hence:

  • The angles do not have the same reference angle.

For more on angles, you can check https://brainly.com/question/24787111

sdestinyheath

Answer:

A

Step-by-step explanation:

A

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