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SAT Math: How Many Radians Are Represented in a Specific Section of a Circle? 5 Views


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Description:

If M represents the origin, how many radians does ∠LMN measure?


Transcript

00:00

Yeah Whoa Okay S a T mash members We've gotta

00:05

figure here and note They tell us it's not drawn

00:08

to scale If M represents the origin how many radiance

00:14

does LMN measure Imagine taking a slice of pie from

00:20

this circle right there with a crust right there Some

00:23

ice cream That's what we're going to do to solve

00:25

this problem So hidden within the deliciousness of the pie

00:29

is a right triangle right there We don't have the

00:31

angle measurements but we do have the sides The X

00:34

value which is one shows how long the horizontal leg

00:37

is The same goes for the Y value and the

00:40

vertical leg there See it looks like this That's the

00:42

triangle So there are two sides that are congruent that

00:46

means with grew And so the angles opposite to those

00:49

sides both marked a for angle also have to be

00:52

equal That corner is already ninety degrees and all angles

00:55

of a triangle add up to one hundred eighty degrees

00:57

Right So the two angles A have to add up

01:00

to ninety degrees So they must both be ninety divided

01:03

by two Yes forty five degrees each This is special

01:06

Forty five forty five ninety Triangle and L M n

01:09

here is forty five degrees but we need to convert

01:12

it to Radi ans How do we do that Well

01:14

forty five degrees times pi radio hands over one eighty

01:17

is pi over four radiance LMN measures pi over four

01:22

radiant So the answer is B And that very helpful

01:25

proportion we used is something needed to solve a whole

01:28

host of trigonometry problems One hundred eighty degrees is equal

01:31

to hi radiance forever Never the units of degrees cancel

01:34

because they're both in the numerator and denominator See how

01:37

that works there While we're here convert the other answer

01:40

choices too if you want right pie over six is

01:42

thirty degrees Power three sixty and over two is ninety 00:01:46.49 --> [endTime] and you know the correct answers can taste good

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