which of the following equations would transform the tangent graph to the parent cotangent graph?\n$y =…

Explanation:

Step1: Recall the relationship between tangent and cotangent

The cotangent function $y = \cot(x)=\tan\left(x +\frac{\pi}{2}\right)$.

Step2: Analyze each option

• Option 1: $y=\tan\left(x+\frac{\pi}{2}\right)$ is the correct transformation as it directly gives the relationship between tangent and cotangent.
• Option 2: $y =-\tan(x - \pi)=-\tan x$ (using the periodicity of tangent $\tan(x-\pi)=\tan x$), not a transformation to cotangent.
• Option 3: $y=-\tan\left(-x-\frac{\pi}{2}\right)=\tan\left(x +\frac{\pi}{2}\right)$ (using $\tan(-\alpha)=-\tan\alpha$), but we are looking for the most straightforward form.
• Option 4: $y=-\tan\left(x-\frac{\pi}{2}\right)=\cot x$ (using trig - identity $\tan\left(x-\frac{\pi}{2}\right)=-\cot x$), but the most direct transformation from tangent to cotangent is $y = \tan\left(x+\frac{\pi}{2}\right)$.

Answer:

$y=\tan\left(x+\frac{\pi}{2}\right)$