anonymous
  • anonymous
Find COS 23pi/6?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
Do you have a calculator?
anonymous
  • anonymous
no
anonymous
  • anonymous
π=180∘

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anonymous
  • anonymous
so I replace pi with 180?
anonymous
  • anonymous
yes
anonymous
  • anonymous
so it'd be 23*pi divided by 6?
anonymous
  • anonymous
exactly (:
anonymous
  • anonymous
thanks :)
anonymous
  • anonymous
welcome (:
anonymous
  • anonymous
Is 12.03 Right?
anonymous
  • anonymous
cosine of a value cannot be larger than 1...
anonymous
  • anonymous
can you please explain?
anonymous
  • anonymous
See the graph of cosine:|dw:1389756073553:dw|
anonymous
  • anonymous
yes
anonymous
  • anonymous
Maximum of a y=cos x function is 1. Minimum of a y=cosx function is -1
anonymous
  • anonymous
so do I need to graph this?
anonymous
  • anonymous
|dw:1389756066410:dw|
anonymous
  • anonymous
So, you cannot have COS 23pi/6 = 12.03
anonymous
  • anonymous
\[\cos\frac{23\pi}{6} = \cos(3(2\pi) + \frac{5\pi}{6}) = \cos\frac{5\pi}{6} = ...?\]
anonymous
  • anonymous
Using the attached drawing where does 23/pi fall?
anonymous
  • anonymous
Okay sir's let me tell you that. Cos23pi/6 -2pi will give you the same answer
anonymous
  • anonymous
idk where 23/pi falls
anonymous
  • anonymous
Subtract 2pi from it
anonymous
  • anonymous
The reason you don't know where it falls is becomes you have to do more than one revolution around the circle
anonymous
  • anonymous
so i subtract 2pi fom 6?
anonymous
  • anonymous
2pi = 12pi/6..So 23pi/6-12pi/6 = 11pi/6
anonymous
  • anonymous
Okay good.
anonymous
  • anonymous
Are you familiar with the unit circle in trigonometry?
anonymous
  • anonymous
Now if radians are bothering you we can convert it to degrees.
anonymous
  • anonymous
do i need like a specific calculator for this?
anonymous
  • anonymous
yes Please
anonymous
  • anonymous
You could plug this into your calculator, but if this comes up on a test and you can't use one, you will be screwed.
anonymous
  • anonymous
11pi/6*180/pi
anonymous
  • anonymous
Can you explain how to do it manually?
anonymous
  • anonymous
That gives us 330 degrees
anonymous
  • anonymous
Do you know where that is on the unit circle?
anonymous
  • anonymous
hint: It's in quadrant IV
anonymous
  • anonymous
yes
anonymous
  • anonymous
Okay. tell me the coordinates for it.
anonymous
  • anonymous
sqrt 2/2, -sqrt 2/2
anonymous
  • anonymous
Not quite.
anonymous
  • anonymous
That would be 315 degrees.
anonymous
  • anonymous
ummm sqrt 3/2 , -1/2
anonymous
  • anonymous
yes. sqrt(3)/2, -1/2
anonymous
  • anonymous
Okay. You should know that Cosx= x
anonymous
  • anonymous
So what is the value for Cos330?
anonymous
  • anonymous
I got -.991...
anonymous
  • anonymous
Keep this exact. You just gave me the coordinates. and I just told you CosƟ=x
anonymous
  • anonymous
so what is the exact answer?
anonymous
  • anonymous
hint: (x,y)
anonymous
  • anonymous
Use the coordinates you gave me.
anonymous
  • anonymous
sqrt 3/2 , -1/2
anonymous
  • anonymous
Yes and I told you cosƟ=x so what is cos330?
anonymous
  • anonymous
I don't get it /.\ I'm sorry
anonymous
  • anonymous
when I plug in Cos330 it gives me the decimal I gave you
anonymous
  • anonymous
|dw:1389757103607:dw|
anonymous
  • anonymous
Okay also cosƟ=A/H This is the unit circle and the hypotenuse will always be one so basically cosƟ=H what is Cos330?
anonymous
  • anonymous
ygarcia what calculator are you using btw?
anonymous
  • anonymous
I don't have a calculator
anonymous
  • anonymous
Okay. Well just finish it. Cos330=A. What is A in that triangle? A for adjacent to theta.
anonymous
  • anonymous
-1/2?
anonymous
  • anonymous
|dw:1389757356882:dw|
anonymous
  • anonymous
No. Adjacent means next to. So what is next to theta that isn't the hypotenuse. -1/2 is opposite.
anonymous
  • anonymous
sqrt 3/2
anonymous
  • anonymous
There you go.
anonymous
  • anonymous
so the solution is sqrt 3/2?
anonymous
  • anonymous
cos330=Sqrt(3)/2
anonymous
  • anonymous
Yes
anonymous
  • anonymous
Now let's see if you learned anything. Tell me the sin330 if you know that sinƟ=y
anonymous
  • anonymous
-1/2
anonymous
  • anonymous
Very good. Just use the coordinates you gave me for that degree value. (sqrt(3)/2, -1/2) (x,y) SinƟ=y and the y value for 330 is -1/2 so that's the answer.
anonymous
  • anonymous
So Cos= x value and Sin= y value?
anonymous
  • anonymous
In reference to the circle
anonymous
  • anonymous
Yeah. Because in the unit circle the radius is one, that's why it's called a unit circle, one unit. Anytime you have something over 1 It's just whatever the numerator is.
anonymous
  • anonymous
Okay, Thanks SO MUCH!!!! I don't fully get it yet but what you explained to me helped A LOT :)
anonymous
  • anonymous
You're welcome.

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