How to find the range of f(x)=1/sinx, and how to know how to draw it

  see the attached for a graph

  the range is (-∞, 1] ∪ [1, ∞)

Step-by-step explanation:

You know the range of the sine function is [-1, 1], including zero. So, the minimum absolute value of 1/sin(x) will be 1/1 = 1, and it will go up from there (or down from -1) toward infinity. The vertical asymptotes will be where sin(x) = 0, at multiples of π.

To graph it by hand, you can pick a few points in any quadrant of the sine function and find their inverses. Plot those. You can take advantage of the symmetry about π/2 and about the origin. You can also take advantage of the periodicity.

A graph is attached.

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step-by-step explanation: