Find COS 23pi/6?

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Find COS 23pi/6?

Mathematics
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Do you have a calculator?
no
π=180∘

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Other answers:

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

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