WEBVTT
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to asks us to sketch the graph of the function
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below. Why equals Cosi kin of two pi X
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. Now, before we can scratch this or sketch
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this graph, we should break it down to really
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see what it means. Well, we know the
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coast seeking is the same as one over sign so
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we can write this function in the alternate form one
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over sign of two pi X. Now we want
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to find the period of our CO c can function
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because we need that if we're gonna sketch it.
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So looking at sign, we know that the period
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is always the same as B. Oops did that
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wrong? Excuse me? The period is the same
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as two pi divided by the absolute value of B
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. And in this instance, B equals two piles
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. So our period will be two pi divided by
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two pi which equals one. And now, although
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I said that was for sign, that extends over
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to our co c can function. So we know
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that the period of our graph is gonna be one
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now, a really interesting or cool technique you can
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use to graft. Cose Eakin is by first initially
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graphing um, sign. So we're gonna make the
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graph of sign of two pi X. We know
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that the amplitude is equal to one because there's nothing
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ah, trailing at the beginning of our checking a
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metric function. So that is gonna make this a
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lot simpler. Um, so first I'm gonna begin
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by in blue graphing sign of two pi X.
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It's just a sketch. So right, the general
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idea down goes like this, all right? And
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we know that at each of these, uh,
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that's one That's two. That's me. I would
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say that this is Thank you, Warren, and
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so on. So each one of these is a
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period of our function, all right, Now,
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because we're supposed to be graphing Coast seeking to pi
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X, everywhere that are signed function equals zero.
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There's going to be an ass motto, and so
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we could see that easily by just looking at where
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our sine function intersex the X axis. So I'm
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gonna come through and draw these yellow dash lines everywhere
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There's going to be on asked meto which is really
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nice, really good visual, way off. Like
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seeing how to graft. Cassie can sense it makes
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it really obvious where our function is undefined everywhere the
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same crosses or equal zero. And I'll do that
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for their that much. Now, in green.
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I'm gonna come in here and I'm gonna draw secret
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graph. Now, everywhere that are sine function has
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a maximum value. That's gonna become a new minimum
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value, all right, approaching the values and they
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are touching right there. A positive one, which
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is in the negative one. And this continues this
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periodic behavior. Since it's a periodic function, we'll
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continue forever in the positive and negative directions. Uh
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huh, Yeah. And just know, they thes
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maximum values right here. All at y equals one
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. And then these other values don't hear all that
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. Negative one. Okay. And so there you
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have it. That is a sketch of the graph
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of CO seeking to pi X.