How to Use the Unit Circle (Explanation #1)
How to Use the Unit Circle (Explanation #1)
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1.38 -> over the next couple of videos I will be
explaining the unit circle in multiple
5.4 -> different ways here is the first way let's go find
a unit circle on the web this is a unit circle in
12.12 -> public domain so let's use this we will begin
in 15 seconds but let me first say this first
19.5 -> explanation is going to be about using the unit
circle to find sine and cosine of many different
26.22 -> angles it's not going to be about why the unit
circle works or anything deep like that I'll
31.98 -> explain that in the later explanations all right
let's go what is sine of 30 degrees how do we
40.56 -> find that on the unit circle all right so first we
find 30 degrees on the unit circle it's right here
47.34 -> then we find the point that is next to it
here's the point and there are coordinates
53.22 -> written here these are actual coordinates right
like this this is the x coordinate this is the
59.22 -> y-coordinate right because we have an x-axis we
have a y-axis right we are on a graph right so
67.44 -> our points have coordinates okay so uh what
I'm about to say is really really important
73.86 -> sine is the y-coordinate sine is always going to
be the y-coordinate so the answer here is a half
82.32 -> okay let's do another one what's sine of 45
degrees 45 degrees well we find 45 degrees on
91.14 -> the unit circle and uh that is right here then
we find the point that is next to it right there
99.3 -> and then here are the coordinates sine
is going to be the y-coordinate right so
105.54 -> this is this is kind of weird because the x
coordinate and the y coordinate are the same
109.56 -> but yeah so sine is going to be square root of 2
over 2. let's do one more let's do the sine of 120
120.12 -> degrees so first we find 120 degrees on the unit
circle it's right here here's the point here are
128.34 -> the coordinates sine is always the y-coordinate
so the answer is square root of 3 over 2. so
136.62 -> what should your main takeaway be here the sign
of any angle I guess I'll write the word angle
145.74 -> is y it's the y coordinate it's always the y
coordinate let's talk about cosine so how would
153.84 -> I find the cosine of like 30 degrees using the
unit circle how would I do that well it's going
161.04 -> to be just like finding the sine of 30 degrees
there's just one difference and that is cosine is
167.28 -> the x coordinate cosine is always the x coordinate
so okay let's find 30 degrees on the unit circle
173.28 -> first it's right there next let's find the point
there's a point here are the coordinates and then
180.96 -> cosine is always the x coordinate cosine is always
the x coordinate so the answer is the square root
187.26 -> of 3 over 2. okay let's do another one cosine
of 45 degrees so first let's find 45 degrees on
195.96 -> the unit circle now let's find the point that's
next to it and here are the coordinates cosine is
201.96 -> always the x coordinate so the answer is square
root of 2 over 2. and then what about cosine of
209.88 -> 120 degrees how would you do that well let's
find 120 degrees on the unit circle and here's
217.14 -> the point next to it here are the coordinates
cosine is the x coordinate right the x coordinate
224.22 -> so negative a half is the answer so what should be
your main takeaway from this cosine of any angle
234.84 -> is the x coordinate it's always the x coordinate
of the point all right that's it for explanation
242.88 -> number one there are more explanations
in the next videos thanks for watching
Source: https://www.youtube.com/watch?v=HFGs6lOezDU