Question

At which value will the graph of y=csc x have a zero

Answer 1

y = csc(x) does not have any zero.

Explanation:

If we have:

y = f(x)

a zero of that function would be a value x' such that:

y = f(x') = 0

Here we basically want to solve:

y = csc(x) = 0

First, remember that:

csc(x) = 1/sin(x)

now, the values of sin(x) range from -1 to 1.

So we want to solve:

1/sin(x) = 0

notice that a fraction:

a/b = 0

only if a = 0.

Then is easy to see that for our equation:

1/sin(x) = 0

The numerator is different than zero, then the equation never will be equal to zero.

Then:

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

Does not have a zero.