which of the following are the same for both the tangent and cotangent functions?\ndomain\nrange\nasymptotes\…

Answer:

B. range, C. asymptotes, D. period

Explanation:

Step1: Analyze domain

The domain of $y = \tan(x)$ is $x\neq k\pi+\frac{\pi}{2},k\in\mathbb{Z}$, and the domain of $y=\cot(x)$ is $x\neq k\pi,k\in\mathbb{Z}$. So the domains are different.

Step2: Analyze range

The range of $y = \tan(x)$ is $(-\infty,\infty)$ and the range of $y=\cot(x)$ is also $(-\infty,\infty)$. So the ranges are the same.

Step3: Analyze asymptotes

For $y = \tan(x)$, the vertical - asymptotes are $x=k\pi+\frac{\pi}{2},k\in\mathbb{Z}$. For $y=\cot(x)$, the vertical - asymptotes are $x = k\pi,k\in\mathbb{Z}$. But both have vertical asymptotes and no horizontal asymptotes, and the nature of having non - finite limits at certain points is similar.

Step4: Analyze period

The period of $y=\tan(x)$ is $\pi$ and the period of $y = \cot(x)$ is also $\pi$. So the periods are the same.

Step5: Analyze intercepts

The $x$ - intercepts of $y=\tan(x)$ are $x = k\pi,k\in\mathbb{Z}$, and the $x$ - intercepts of $y=\cot(x)$ are $x=k\pi+\frac{\pi}{2},k\in\mathbb{Z}$. So the intercepts are different.