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Sam: I'm back! Mike: Thanks, Sam.
Mike: So what's our assignment today? Mary: Hopefully it's not English again...
Sam: Hey, I think English is really fun to teach!
Mike: Okay...
Mike: Try saying "soy" as in soybeans. Sam: Fine...
Sam: Swah... Swahbeans... swah swah swah...
Sam: I'll get it eventually.
Sam: Anyway we need to teach something for math class. We get to choose the topic
Mary: How about division by zer- Sam: NO!
Sam: Don't tell them anything about that!
Sam: it may cause a black hole! Mike: What about sectors? sectors
Mike: That's easy enough, right? Mary: Actually that sounds great! sounds great
Mary: Let's talk about sectors.
(Transition)
Mary: A sector is the area between an arc and 2 radii of a circle. Mike: In simpler terms,
Mike: It's a slice of the a circle...
Mike: kind of like a piece of pizza.
Mike: A minor sector has an angle measure of less than one-eighty.
Mike: This means the angle formed by the two radii is less than half of the circle's
Mike: total three-sixty degrees.
Mary: A major sector is the opposite of that
Mary: It's a sector with an an angle of more than 180. Mike: Sam,
Mike: We've been saying most of the stuff, it's your turn.
Sam: Oh, the sides of the sector are the same length.
Sam: This can be proved because all radii of a circle are congruent.
Sam: It's like... Inception.
Mike and Mary: STOP IT!
Mike: Now let's move on to the length of the arc formed in a sector
Mike: It's actually really easy, assuming you have the angle of the sector, all you
Mike: need to do is find the circumference and get a fraction of its based on that
Mike: angle.
Mary: Let's use this circle as an example
Mary: the sector is shown to have a ninety degree angle
Mary: it has side lengths of 4.
Mary: we know that the circumference of the circle can be calculated with diameter
Mary: π, or 2πr.
Mike: Thus, the circum. of this circle is 8 π, or 8 mult. by whatever
Mike: pi value you had been instructed to be used by your teacher.
Mary: the measure of the circle is three sixty degrees, and ninety over three-sixty is
Mary: congruent to 1/4
Mary: All we have to do now is divide the circumference by 4.
and, of course, eight π divided by four is... 2 π
Mike: So there you have it
the arc length of this sector is 2 π.
Sam: You need to be able to find the circumference and area of the circle in
order to find both the area and arc length for the sector.
Mike: What was that?
Mary: Whatever it was, it's a good idea to remember how to find the circumference
and area of circles.
Sam: Now, how do we find the area of sectors
Mike: Actually,
Mike: that's really easy as well! Again you'll find the fraction of the central angle
of the sector to three-sixty. but this time you multiply it by the area of the
circle.
Sam: Okay, that's getting repetitive.
Mike: Let's use the same circle.
Mike: We take the radius of the circle
and square it.
4 squared equals sixteen.
Our area is sixteen π or multiply sixteen by...
(Pi Song)
Sam: But that's not all.
Mary: Nice catch! We still need to multiply it by the
fraction. we already know that ninety over three sixty is 1/4 so we just
need to divide sixteen π by 4 resulting in four π as the sector's
area.
Mike: That's essentially all you need to know about sectors.
Mike: Sectors are also commonly referred to as wedges.
Sam: The central angle of a sector is sometimes referred to as theta.
Theta is the 8th letter of the Greek alphabet.
It looks kind of like a zero with a line drawn through it.
Mary: It's better to leave the value of circles as value multiplied by pi.
Pi is an irrational number.
Its value was approximated by Archimedes.
Mike: Archimedes? That guy who shouted "Eureka" and ran through Greece naked?
Mike: That's all for today
Sam: We should have done this in a more retro way.
Sam: NO!
that's a horrible song!
Mary: I like it
Mike: Everyone is entitled to their own opinion