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Attributes of Circles
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This video can run circles around other videos about circles. Sir Cumference, of Round Table fame, explains all the properties of… well, circles....

1
Perimeter and Circumference
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It's super useful to be able to find the distance around stuff. Like when you’re being pursued by authorities while running around the base of an...

2
Area of a Sector
2665 Views

Time to learn about the area of a sector. And no, that's not the sector's bedroom with a bumper sticker on the door that reads, "GO AWAY."

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Tangent Half-Angle Formula 1362 Views


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Description:

Mosquitos need their caffeine, just like the rest of us. Wouldn't think zipping around and stinging people all day long sap your energy?

Language:
English Language

Transcript

00:04

Tangent Half Angle Formula, a la Shmoop. Vido the Mosquito is exhausted after returning

00:12

from his business trip to Trigonometry Springs. Vido desperately needs an espresso. At Jolts

00:19

and Volts Coffee he orders his much needed jolt of caffeine.

00:23

As Vido digs in his pockets for theÉtangent of pi over eightÉ dollars he needs to pay

00:30

for his double shotÉ Éhe realizes he is in Half Angle-os and he

00:34

only has Trig Springs money. In Half Angle-os, all money is converted using

00:44

the following formula: Tangent of u over 2 equals one minus the cosine

00:50

of u over sine of u. How will Vido convert his money to the correct

00:56

amount for his much needed coffee? First of all we can see that tangent of pi

01:01

over 8 can be rewritten as ? times pi over 4.

01:06

If we do this, we can get rid of the denominator 2 in our formula.

01:10

Then, if we substitute tangent of pi over 4 in for u, we get the following:

01:15

1 minus cosine of pi over 4 all divided by sine of pi over 4.

01:23

Since cosine of pi over 4 equals the square root of 2 over 2, and the sine of pi over

01:29

4 equals the square root of 2 over 2É Éour formula becomes:

01:33

1 minus the square root of 2 over 2 all over square root of 2 over 2.

01:40

Having too many terms just brings troubleÉ Éso first, to simplify the numerator, we

01:44

can put both terms under the same common denominator. Let's do this by multiplying 1 by 2 over 2,

01:50

to get 2 over 2 minus root 2 over 2. We subtract fractions by subtracting across

01:57

the numerator of the fractions and keeping the denominator the same, so we get 2 minus

02:03

root 2 over 2 on the top of the bigger fraction. We hate fractions in the denominator, so letÕs

02:12

multiply the numerator, 2 minus root 2 over 2É by the reciprocal of the denominator to

02:18

get rid of it. The 2 in the numerator and denominator cancel

02:23

out, so we're left with 2 minus root 2 divided by root 2.

02:27

We canÕt have radicals in the denominator, so we will rationalize it by multiplying the

02:32

fraction by root 2 over root 2. This gives us the fraction root 2 times the

02:38

quantity 2 minus root 2 all over 2. To simplify, letÕs distribute the root 2

02:45

across the quantity 2 minus root 2 to get 2 root 2 minus 2 all divided by 2.

02:52

Since we have a 2 on top and a 2 on bottom, they cancel each other out, so our final quantity

02:57

is root 2 minus 1. Fed up with having to go through so much math,

03:01

Vido throws his money at the barista and demands his coffee.

03:05

The barista calmly reaches back and points to a sign saying ÒWe reserve the right to

03:10

refuse service to anyone.Ó Maybe try the Starbugs across the street,

03:15

Vido.

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