# Question Video: Graphing Reciprocal Trigonometric Functions Mathematics • 10th Grade

Identify the graph of ๐ฆ = cot ๐ฅ.

02:45

### Video Transcript

Identify the graph of ๐ฆ equals cotangent of ๐ฅ.

When we look at these three graphs, we know by their shape that theyโre all representing either tangent or cotangent. To correctly identify the graph, weโll need to know some test points. For example, what is the cotangent of ๐?

Two of these graphs have the cotangent of ๐ approaching โ, but one of them has the cotangent of ๐ at zero. If you plug in the cotangent of ๐ฆ on any technology, itโs going to tell you โundefinedโ; it does not exist at that point. We havenโt eliminated the red or the yellow graph. We can eliminate this blue graph because the point ๐, zero does not fall in cotangent of ๐. Cotangent of ๐ is not equal to zero.

Now, letโs zoom in a little bit closer on the red and yellow graph. Halfway between zero and ๐, both of these graphs are at point zero. And that means that ๐ over two is equal to zero in both of these graphs. Both of these graphs share all of their ๐ฅ-intercepts. We need another way to determine the differences. So weโre going to check the places where ๐ฆ equals one. For both of these functions, what is ๐ฅ equal to if ๐ฆ equals one?

We assume the formula of cotangent ๐ฅ in both cases. And we want to know what ๐ฅ-value would make the outcome one. If we take the cotangent inverse of one, weโll find out what ๐ฅ should be. The cotangent inverse of one equals ๐ over four. We need to look at ๐ over four for our ๐ฅ-value.

Here it is on the red graph, and here it is on the yellow graph. ๐ over four, one is a point on the yellow graph. There is not a point at ๐ over four, one on the red graph. This means that the red graph is not a graph of ๐ฆ equals the cotangent of ๐ฅ, only the yellow graph was.