WEBVTT
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problem. Number 58 asks us to create a sketch
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of the following function. Why equals to tension of
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X? Now, before we begin, I want
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to point out that why equals Tangent of X is
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also equal to sign of X over coastline of X
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. And this breaking the formula done into this is
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really important because it allows us to understand a really
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, uh, characteristic aspect of tangents. Graff And
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that is that tangent has Assam a totes in its
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graph and ask him a toaster points where our function
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does not have a defined value. And so when
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we look at our this expression for tangent sine over
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co sign, we see that because there is co
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sign of the denominator whenever it's equal to pi halfs
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, it's going to be undefined because cosign a pi
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house zero. So I'm gonna go through here and
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break up our number line into increments of pi house
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and because we know already know that at these points
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our function is going to be undefined. I'm gonna
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go ahead and draw some dotted lines just so we
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have a better visual of these ass mottos. So
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this is the first crucial part of drawing this function
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. They're with me here while I get these lines
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in. All right, That should be good now
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, because there's nothing inside of our triggered a metric
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function y equals tangent of X. We know that
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the period is just going to be the standard period
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of, um hi. Because the period of Tanja
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is equal too high over the absolute value of being
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and in this instance be is one. So our
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period is pie, huh? I just realized I
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made an error. Excuse that, please. So
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, yes, at increments of pie and two point
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, there will not be as mottos sound. It's
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a good thing to catch. And now if we
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look at this other term, our this other aspect
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of our equation this too. We see that it's
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multiplied toward Tanja necks. And when we have graft
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signing coastline, we see that that changes the amplitude
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. But in the context of tangent, it doesn't
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necessarily change the amplitude because tangent extends both from negative
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infinity operate a positive infinity so that to that constant
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of the front is pretty much just increasing the rate
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at which are tangent. Graft grows to infinity So
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I'm gonna come in here now, and I'm just
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gonna draw tangent as it is approaching these Asamoah Taub's
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because it's periodic will see that this behavior repeats for
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every period going in the positive, infinite direction and
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also going in the negative direction may have it.
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That's a graph for why equals tangent of