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NationalTutoringObservatory
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MathEd-PII

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student
It’s called trigonometric functions of acute angles
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student
That’s the topic name
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volunteer
ok. Can you show me a problem that you are working on?
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student
Can you teach me topic wise my school just started
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volunteer
What have you learned so far?
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student
Supplementary and complementary angles standard position quadrant of an angle
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volunteer
Sorry, I don't have a lesson planned for this. As a tutor, I usually help students with their homework. It might be better if you made another request. Sorry.
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student
I can get back to you tomorrow with the homework
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volunteer
Sounds good.
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volunteer
Have a good evening.
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student
You too thanks
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volunteer
you are welcome.
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volunteer
bye
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student
hi! how are you?
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volunteer
Liam!
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volunteer
good how r u?
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student
I'm good too
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volunteer
what do u need help with?
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student
I was wondering if you could help me with an algebra assignment
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volunteer
yea sure
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volunteer
do u know how long it will take
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volunteer
aprox
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student
I only have one question I need help with
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volunteer
oh ok
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volunteer
what is it?
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volunteer
can u make it a ittle bigger?
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volunteer
thanks
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volunteer
do u know what to do to find x-intercepts?
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student
she didn't really explain it well when I was in class
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volunteer
set y=0
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volunteer
or in this case f(x)
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student
ok
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volunteer
so u can solve for x
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volunteer
ill write it
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volunteer
can u see that?
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student
yes
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volunteer
can u solve for x?
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student
k
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student
7/3 and -3
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volunteer
yes!!
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volunteer
so thats ur answer for A B and C
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volunteer
does it make sense?
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student
yes
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volunteer
do u want to try doing D by urself?
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volunteer
or do u need help?
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student
-7?
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volunteer
Yes!!
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student
:)
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volunteer
u got it!!
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student
thank you!
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volunteer
does it make sense tho?
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student
yes
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volunteer
ok :)
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student
I hope you have a good night
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volunteer
u too
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student
hi could you help me out with this?
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volunteer
Hi How are you?
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student
good
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volunteer
Ok. Let's see your integral.
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student
this is all ive got so far
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volunteer
Ok. Give me a couple of minutes to think on this.
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student
ok
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volunteer
It's clear that the base can be represented by r^2 + y^2, since it is a circle. Do you agree?
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student
yea
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volunteer
Now each "square" It seems to me, has a side equal to 2r. What do you think about that?
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student
yea i agree
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volunteer
Ok. So I think we need another relation ship to set up the integral. Any thoughts?
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student
that area of the squares is s^2
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volunteer
So. In this case each "square" has an area of 4r^2.
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student
why
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volunteer
Well, if we agree that each side of the square is 2r, then the area of a representative square would be (2r)(2r) = 4r^2
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student
ohh yes ok
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volunteer
Now. We already know that r^2 = x^2 + y^2
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volunteer
What we need is some relationship between x and y so that we can integrate over one variable.
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volunteer
Give me a couple of minutes to ponder that please,
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student
ok
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volunteer
Alright. I think we were close. Just a bit off.
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volunteer
So the circle is x^2 + y^2 = r^2
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volunteer
But the side of each square is really 2y, not 2r. r is a constant, so that doesn't work. Do you follow?
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student
ohh yea i see
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student
so the vertical y values change
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volunteer
Exactly.
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volunteer
So let's set up our integral to be a(x) = (2y)^2 = 4y^2 dx.
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volunteer
But y^2 = (r^2 - x^2)
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volunteer
So. You get Int(r^2 - x^2) dx over the limits.
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volunteer
Would you write the integral on the whiteboard please?
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student
ok
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student
like this?
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volunteer
Excellent. Let's talk about the limits now.
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student
im still kind of confused why we got 2y again where did the 2 come from
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volunteer
Ok let's back up.
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volunteer
Take a look at the diagram again and focus on the squares.
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student
ok
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volunteer
Each one varies as shown by the vertical slices in the diagram.
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student
yea
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volunteer
Now. If you focus on a typical square, especially the one at the center, you will see that it is the same as the diameter of the circle. That one is 2r for each side.
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volunteer
The other ones are smaller, as you look at slices off the center.
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volunteer
The relationship to determine the length of the other ones is (r^2 - y^2)^(1/2).
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volunteer
Is that making any sense?
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student
yes so that's = x?
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