### Video Transcript

Which of the following is the graph of the function ๐ of ๐ฅ equals one divided by the sin of ๐ฅ?

Letโs first plug in some values that we know for the sin of ๐ฅ. The sin of zero is zero. So if we would take our function and plug in zero for ๐ฅ of sin of zero, we know thatโs zero, but one divided by zero, actually anything divided by zero is undefined, so it canโt actually work.

So in these two top graphs, itโs showing values at zero. So when ๐ฅ is zero in the blue graph, weโre at around one, and then in the green graph, at zero, weโre at zero. So we can eliminate these.

Something else we can plug in now notice weโre plugging in for ๐ฅ, and our ๐ฅ values are zero, ๐ over two, ๐, three ๐ over two, and two ๐, so we have to plug in values in these ๐s. So letโs plug in ๐ over two. And the sin of ๐ over two is one, so if we plug this into our function, and the sin of ๐ over two is one; one divided by one is one, so at ๐ over two, we should be at one.

In our yellow graph, when weโre at ๐ over two, we get zero for ๐ฆ, so that doesnโt work, but in our red graph, at ๐ over two, weโre at about one. Therefore, this red graph will be the graph of our function.