Question

can someone explain how to get y=3cotx over a one period interval? i need to show my work

Answer 1

Solution-

To get  y=3cot(x) over a one period interval,we firstly draw y=cot(x) over one period interval.

We know that y=cot(x) has a period of π.

So it's one cycle is vary from x=0 to x=π.

At x=0 ,y=cot(0)=+∞

At x=π/4,y=cot(π/4)=1

At x=π/2, y=cot(π/2)=0

At x=3π/4, y=cot(3π/4)=-1

At x=π y=cot(0)=–∞

Using these values, we can know get y=cot(x) over one period interval(as shown in figure below).

Now, to get y=3cot(x), we just need to stretch the graph three times along y-axis.It means

At,x=0, y=3(+∞)=+∞

At x=π/4, y=3(1)=3

At x=π/2, y=3(0)=0

At x=3π/4 , y=3(1)=-3

At x=π, y=3(–∞)=–∞

From these values, we can now get the function y=3cot(x) over one period interval (0,π) (as shown in figure below).