which of the following are the same for both the tangent and cotangent functions?\n□ domain\n□ range\n□…

which of the following are the same for both the tangent and cotangent functions?\n□ domain\n□ range\n□ asymptotes\n□ period\n□ intercepts\ndone

which of the following are the same for both the tangent and cotangent functions?\n□ domain\n□ range\n□ asymptotes\n□ period\n□ intercepts\ndone

Answer

Explanation:

Step1: Recall domain of tangent and cotangent

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

Step2: Recall range of tangent and cotangent

The range of (y = \tan(x)) and (y=\cot(x)) is ((-\infty,\infty)), so range is the same.

Step3: Recall asymptotes of tangent and cotangent

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

Step4: Recall period of tangent and cotangent

The period of (y = \tan(x)) and (y=\cot(x)) is (\pi), so period is the same.

Step5: Recall intercepts of tangent and cotangent

The (x -)intercepts of (y=\tan(x)) are (x = k\pi,k\in\mathbb{Z}), and (y=\cot(x)) has no (x -)intercepts, so intercepts are different.

Answer:

range, period