# How to plot the graph of f(x)=cos (pi/2)?

Jun 26, 2015

I suspect you forgot...$x$!
It is probably $f \left(x\right) = \cos \left(\frac{\pi}{2} x\right)$
As it is the function represents a constant ($\cos \left(\frac{\pi}{2}\right) = 0$), i.e. a horizontal line.

#### Explanation:

If it is $f \left(x\right) = \cos \left(\frac{\pi}{2} x\right)$, you have a cosine in the form:
$f \left(x\right) = A \cos \left(k x\right)$;
of amplitude $A = 1$ and period equal to: $p e r i o d = \frac{2 \pi}{k} = \frac{2 \pi}{\frac{\pi}{2}} = 4$:
Graphically you have for $f \left(x\right) = \cos \left(\frac{\pi}{2} x\right)$:
graph{cos((pi/2)x) [-5.55, 5.547, -2.773, 2.774]}

As you can see one complete oscillation fits between $0$ and $4$ radians and then it repeats itself again (period). The maximum height is $1$ (amplitude).

So, basically, it is a "shrunk" version of a normal $\cos$ (that completes one oscillation in $2 \pi = 6.28$ radians) that you can see in the following graph of $f \left(x\right) = \cos \left(x\right)$:
graph{cos(x) [-5.55, 5.547, -2.773, 2.774]}