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Graphing Trig Functions on TI 83 Calculator

September 11, 2019

This video will go through graphing trig
functions using our TI-83 plus calculator. We’ll show both sine and
cosine, as well as our tangent functions. There’s a few new buttons we’re going to
need to use on our calculator. Hopefully you’re familiar with these from graphing
other types of functions such as linear functions or quadratic functions, but as
a refresher we’ll need the y equal button, and the graph button in order to
enter in graphs, and to actually draw the graphs. We’ll also be using the zoom
button, and we’ll be using the zoom button a little differently than you
have for other types of functions. We’ll also need to use the variable button, or
at least that’s what I call it, it’s the one that’s labeled X, T, theta, and n, and
of course we’ll still have to use our sine, cosine, and tangent buttons, as well
as remember how to use that pi button whenever we’re graphing trig functions.
Let’s first look at something simple such as sine of x. To graph sine of x
we’ll go and hit y equals, and if there was information here, all I would have to
do is hit my Clear button, and I’ll go ahead and press sine, and then my X, T,
theta, n button, or my variable button, and end parentheses and then I’ll
hit graph. And there is my basic sine function. Well, it’s my sine function but
quite frankly, it’s a little bit small and I’m not quite sure how many periods
I’m looking at there. So what I’m going to do is use the zoom button, and I’m
going to use this Ztrig button, and what that will do, is that will give me a good
look in terms of y, in terms of my maximum value of my minimum value, and in terms of my x it will make my window such that I see exactly two complete
cycles of my trig function, because that’s a good thing to look at when
we’re trying to graph these functions, and that’s all there is to it. Again we
use that zoom, and Ztrig in order to show our two complete cycles of our
trigonometric function. Let’s look at something like f of x is equal to
negative cosine of x. Remember, if we multiply
our sine or cosine by a negative 1 what that did was reflect our sine and
cosine over our x-axis, so let’s see if this works. If I hit my y equals button again, and now I’m going to hit my negation button,
and then cosine, and then my variable button, and I close parentheses, and I’ll
go ahead and graph that, then I’ll see yes in fact, this is my basic cosine
function, but it’s now reflected over that x-axis. Now let’s also look at
tangent of x. When we did the transformations we focused on sine and
cosine, but we can also look at graphing tangent. Let’s clear that out, and we’ll
go ahead and graph tangent of x. When I hit graph, we remember that tangent had
those points of disjoint, where it went from positive infinity to negative
infinity. Now if you notice, it almost looks like the function has a value, that
it’s equal to at this point, because we see this line here. That’s only because
if we click on mode, see my calculator’s in connected mode. What this does is it
connects the dots when it graphs a function, it will calculate a bunch of
different points, and just connect those dots. Well if I leave it as a dot, then it
won’t draw a line between my two dots. Hit enter, and then it no longer looks
like it’s actually equal to a value at those points. We can even do something
crazy like add sines and cosines together. For instance if I had a
function sine x plus cosine of 5 x, we could find out what this trig function
looked like using our calculator. All I would do is type in sine x,
being very sure to close my parentheses because I want to add to that, cosine of
5 x. Again I’ll close my parentheses and hit graph, and now we see something
absolutely crazy, but a lot of real-life applications might involve adding two
different sine or cosine functions together. And we can find out what they
would look like by using our calculator. And there we have graphing trig function
on our TI-83 plus calculator. We’ve graphed sine, cosine, and tangent, as well
as adding sine and cosine functions together.

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  • Reply Garras Porgratix July 16, 2010 at 7:30 pm

    PSSST!! PSST! hey, can you speak up?

  • Reply DominoChild February 12, 2011 at 3:34 pm

    I did everything you said in the beginning, but when i go to graph Sin(X) it says "Error Window Range"

  • Reply Dina Yagodich February 12, 2011 at 9:06 pm

    Try to reset your calculator (go to 2nd and Mem — over the + key) and try again. Sometimes your calculator gets into a strange mode. If you still have trouble, go to ZOOM and ZTrig and see if that works.

  • Reply Jacqueline Nunez-Carvajal February 26, 2012 at 9:22 pm

    This is boring.

  • Reply ah7 September 7, 2012 at 2:02 am

    Very helpful! Thanks for explaining about the reset – my calculator wan't graphing anything and the reset seemed to fix it.

  • Reply MyDefendor Q January 7, 2016 at 3:08 am

    How do you put a function with longer periods such as; y=2sin0,8(x-10) how do u put in 0,8?

  • Reply Maria _ April 22, 2016 at 7:16 pm

    To the point! Great video.

  • Reply bilbojumper October 7, 2016 at 3:34 pm

    this was helpful

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