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Identify the graph of π¦ equals cotangent of π₯.
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When we look at these three graphs, we know by their shape that theyβre all representing either tangent or cotangent.
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To correctly identify the graph, weβll need to know some test points.
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For example, what is the cotangent of π?
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Two of these graphs have the cotangent of π approaching β, but one of them has the cotangent of π at zero.
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If you plug in the cotangent of π¦ on any technology, itβs going to tell you βundefinedβ; it does not exist at that point.
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We havenβt eliminated the red or the yellow graph.
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We can eliminate this blue graph because the point π, zero does not fall in cotangent of π.
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Cotangent of π is not equal to zero.
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Now, letβs zoom in a little bit closer on the red and yellow graph.
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Halfway between zero and π, both of these graphs are at point zero.
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And that means that π over two is equal to zero in both of these graphs.
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Both of these graphs share all of their π₯-intercepts.
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We need another way to determine the differences.
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So weβre going to check the places where π¦ equals one.
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For both of these functions, what is π₯ equal to if π¦ equals one?
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We assume the formula of cotangent π₯ in both cases.
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And we want to know what π₯-value would make the outcome one.
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If we take the cotangent inverse of one, weβll find out what π₯ should be.
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The cotangent inverse of one equals π over four.
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We need to look at π over four for our π₯-value.
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Here it is on the red graph, and here it is on the yellow graph.
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π over four, one is a point on the yellow graph.
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There is not a point at π over four, one on the red graph.
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This means that the red graph is not a graph of π¦ equals the cotangent of π₯, only the yellow graph was.