Question

Explain why sketching y=sin(x) can help graph y=csc(x)

Answer 1

y = csc (x) = 1/sin (x)

When you realize that sin (x) is an even function, you can conclude that csc(x) is also even.

Whenyou draw y = sin(x), you will see the zeroes of the function, which are values for which the funcion csc(x) is not defined, but goes to + or - infinity, i.e. you obtain the asymptotes.

You can also realize that the maximums of sin(x) will result in minimums of csc(x).

Answer 2

The graph of csc x is a parabola with its vertex at the node of the graph of sin x.