# How do you graph  y = 3/2 cot( pi/2) x ?

Oct 13, 2015

it is a strait line graph with a very steep positive gradient.

Did you mean $y = \frac{3}{2} \cot \left[\left(\frac{\pi}{2}\right) x\right] = \frac{3}{2} \cot \left(\frac{\pi x}{2}\right)$ ?

#### Explanation:

If you did mean that it should be $\cot \left(\frac{\pi x}{2}\right)$ then this is a very different question!!!
graph of $y = \frac{3}{2} \times \cot \left(\frac{\pi x}{2}\right)$

Consider the presented question of $y = \frac{3}{2} \times \cot \left(\frac{\pi}{2}\right) \times x$

$\frac{3}{2}$ is a constant

$\frac{\pi}{2}$ is a constant so $\cot \left(\frac{\pi}{2}\right)$ is also a constant

The result is that $x$ is multiplied by some constant.

The thing is, are you measuring the angle in degrees or radians?

Note: cot = $\frac{1}{\tan}$ so in effect you have:

$y = \frac{3}{2} \times \frac{x}{\tan \left(\frac{\pi}{2}\right)} = \frac{3 x}{2 \tan \left(\frac{\pi}{2}\right)}$

which may also be written as:

$y = \frac{3}{2 \tan \left(\frac{\pi}{2}\right)} \text{ } x$

If just degrees then you would be looking at:

$y \cong \frac{3}{2 \times 0.055 \ldots} x$

$y \cong 54.7 x$ to 1 decimal place.

If on the other hand you are measuring in radians and we have say $\frac{\pi \text{ radians}}{2}$ then it is $\frac{{180}^{0}}{2} \to \tan \left({90}^{0}\right)$ which is a problem!!!