# How do you find the period of y=cot(x-π/2)?

Mar 17, 2018

The period of the ratio functions are $\pi$

#### Explanation:

The period of $y = \cot \left(x - \frac{\pi}{2}\right)$ is the same because our function is not being modified by anything other than a shift to the right $\frac{\pi}{2}$.

In trig, we have the form $f \left(x\right) = a \cdot t r i g \cdot \left(b x + c\right) + d$. The different coeffecients and their meaning are listed below.

a = Amplitude. In terms of sin/cos, this is what affects the cusps of the graph. for $f \left(x\right) = \sin \left(x\right)$ our range is (-1, 1). If $f \left(x\right) = 3 \sin \left(x\right)$ then our range would be (-3, 3).

b = Periodicity. This is the part that you're looking for. Because this value is 1, the periodicity is unchanged. We can find the period of any trig function by feeding some information into the following equation.

Period = $\left(\frac{\text{Regular interval}}{|} b |\right)$ where B is the coeffecient value of x. The interval of all "non-ratio" functions are $2 \pi$, the ratio functions, tan and cot, are $\pi$

c = Horizontal Shift. In your example this graph will be shifted $\frac{\pi}{2}$ to the right.

d = Vertical Shift. This value will shift the graph up or down to the value of d.