which of the following best explains why $cos\frac{2pi}{3}\neqcos\frac{5pi}{3}$?\nthe angles do not have the…

which of the following best explains why $cos\frac{2pi}{3}\neqcos\frac{5pi}{3}$?\nthe angles do not have the same reference angle.\ncosine is negative in the second quadrant and positive in the fourth quadrant.\ncosine is positive in the second quadrant and negative in the fourth quadrant.\nthe angles do not have the same reference angle or the same sign.

which of the following best explains why $cos\frac{2pi}{3}\neqcos\frac{5pi}{3}$?\nthe angles do not have the same reference angle.\ncosine is negative in the second quadrant and positive in the fourth quadrant.\ncosine is positive in the second quadrant and negative in the fourth quadrant.\nthe angles do not have the same reference angle or the same sign.

Answer

Answer:

B. Cosine is negative in the second quadrant and positive in the fourth quadrant.

Explanation:

Step1: Determine quadrants of angles

The angle $\frac{2\pi}{3}$ is in the second - quadrant ($\frac{\pi}{2}<\frac{2\pi}{3}<\pi$), and $\frac{5\pi}{3}$ is in the fourth - quadrant ($\frac{3\pi}{2}<\frac{5\pi}{3}<2\pi$).

Step2: Recall cosine sign in quadrants

The cosine function has the property that $\cos\theta<0$ in the second quadrant and $\cos\theta > 0$ in the fourth quadrant. So, $\cos\frac{2\pi}{3}<0$ and $\cos\frac{5\pi}{3}>0$, which means $\cos\frac{2\pi}{3}\neq\cos\frac{5\pi}{3}$.