Sine Archives | Every Step Calculus

U Substitution Video: Sine on the TI-89

March 16, 2014 by Tommy Leave a Comment

U Substitution Sine on the TI-89: Raw Transcript

Hello everyone, Tom from everystepcalculus.com and everystepphysics.com, Iím going to do a U substitution problem that a customer sent me regarding sine and letís get started.
Index 7 to get to both menus, both programs are installed and weíre going to go to U substitution in the menu, we are going to enter our function, we have to pres alpha before we enter anything into this entry lines, alpha square root of X times sine of X to the three halves minus one. I always show you what you have entered, here we have square root of X times sine of X to the three halves minus one, notice the parenthesis, you have to use good parenthesis in math, learn that, itís important and I say itís OK, Iíll give you a chance to change it and when weíre evaluating this we rewrite it because this over here, the square root of X over here matches what weíre going to do in the next screen. U we chose is X to the three halves minus 1, the derivative of that is three halves square root of X and we always take the *** from this side and put it over to di divide by three halves, notice when youíre dividing by three halves youíre going to invert that to two thirds, always remember that important step in algebra and math and here is the same, we wrote it over here so we know itís a U substitution problem, if that wasnít the same and you canít make it to be the same then thatís not a U substitution problem and so here is sine of U is equal to sin of this right here which we know and ** with the integral of the sine of U we have du divided by three halves, here we convert it, two third times the integral of U, two third times the derivative of the integral of the sign of U is minus cosine of U plus C, answer is minus two third cosine of this as we substitute back in for U, pretty neat, everystepcalculus.com or everystepphysics.com, go to my site, buy my programs and pass your calculus class.

Sine Taylor Series Solved on TI-89 Video

January 13, 2014 by Tommy Leave a Comment

Sine Taylor Series Solved on TI-89: Raw Transcript

Okay this is Tom from every step
calculus dot com I’m gonna do the Taylor series with
sin of X
and let’s get started you put index
9 into the entry line here
the and I give you instructions on how to do that
press ENTER here and we’re gonna scroll down to
I going to scroll up because closer to the end of the alphabet then in the middle
and I’m gonna go to Taylor
maclaurin and press Enter
and
the ask for if they ask for maclaurin and then you’re gonna put zero in for a
otherwise you can put any number in for a actually a
is the X value on the function that you’re gonna
approximate the slope of a line at
here’s a formula for the Maclaurin series
and
for the Taylor series right these all on your paper all the time
look like a genius enter the…you have to
press alpha first before we do anything on our entry lines here’s I’m going to Press alpha
and let’s see sine
second sine of
X close up parentheses
press enter
and centered at let’s say
3 alpha
3 I always show you what you’ve entered, you can change it if you want I say it’s okay
here’s the formula it’s a Taylor series because it’s not zero for a
understand they have to be derivatives have to be
on going one after the other
that’s part of the Taylor series working
write this on your paper this is the first five derivatives of that
and then we’re going to compute the
derivatives at 3 the point we want the
slope of a line to be in that function
and we’re going to have a factorial here 2_3_4_5
to be computed at that we’ve come up with these answers here
write all this on your paper it’s all-important
and here’s the answer
cosine of 3 x minus 3
minus sin of 3 times x
minus 3 squared divided by 2 divide by 6 by 24 by 20
Pretty neat huh, every step calculus dot
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