Question

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.

Answer 1

Using the tangent equation and reference angles, it is found that the correct option is given by:

The angles do not have the same reference angle.

What is the tangent of angle?

It is given by the sine divided by the cosine. For angles that are not on the first quadrant, we can also finding their tangent by using their reference angles, considering the signs according to the quadrant of the angles.

Angle $\frac{5\pi}{6}$ is on the second quadrant, and the reference angle is:

$\pi - \frac{5\pi}{6} = \frac{6\pi}{6} - \frac{5\pi}{6} = \frac{\pi}{6}$

Angle $\frac{5\pi}{3}$ is on the fourth quadrant, and the reference angle is:

$2\pi - \frac{5\pi}{3} = \frac{6\pi}{3} - \frac{5\pi}{3} = \frac{\pi}{3}$

Different reference angles, hence different values for sine and cosine, and different value for the tangent.

Both $\frac{5\pi}{3}$ and $\frac{5\pi}{6}$ are positive measures, hence the only reason is the difference reference angles.

More can be learned about reference angles at brainly.com/question/14910565

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