Find COS 23pi/6?

- anonymous

Find COS 23pi/6?

- katieb

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- anonymous

Do you have a calculator?

- anonymous

no

- anonymous

π=180∘

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## More answers

- anonymous

so I replace pi with 180?

- anonymous

yes

- anonymous

so it'd be 23*pi divided by 6?

- anonymous

exactly (:

- anonymous

thanks :)

- anonymous

welcome (:

- anonymous

Is 12.03 Right?

- anonymous

cosine of a value cannot be larger than 1...

- anonymous

can you please explain?

- anonymous

See the graph of cosine:|dw:1389756073553:dw|

- anonymous

yes

- anonymous

Maximum of a y=cos x function is 1. Minimum of a y=cosx function is -1

- anonymous

so do I need to graph this?

- anonymous

|dw:1389756066410:dw|

- anonymous

So, you cannot have COS 23pi/6 = 12.03

- anonymous

\[\cos\frac{23\pi}{6} = \cos(3(2\pi) + \frac{5\pi}{6}) = \cos\frac{5\pi}{6} = ...?\]

- anonymous

Using the attached drawing where does 23/pi fall?

- anonymous

Okay sir's let me tell you that.
Cos23pi/6 -2pi will give you the same answer

- anonymous

idk where 23/pi falls

- anonymous

Subtract 2pi from it

- anonymous

The reason you don't know where it falls is becomes you have to do more than one revolution around the circle

- anonymous

so i subtract 2pi fom 6?

- anonymous

2pi = 12pi/6..So 23pi/6-12pi/6 = 11pi/6

- anonymous

Okay good.

- anonymous

Are you familiar with the unit circle in trigonometry?

- anonymous

Now if radians are bothering you we can convert it to degrees.

- anonymous

do i need like a specific calculator for this?

- anonymous

yes Please

- 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

11pi/6*180/pi

- anonymous

Can you explain how to do it manually?

- anonymous

That gives us 330 degrees

- anonymous

Do you know where that is on the unit circle?

- anonymous

hint: It's in quadrant IV

- anonymous

yes

- anonymous

Okay. tell me the coordinates for it.

- anonymous

sqrt 2/2, -sqrt 2/2

- anonymous

Not quite.

- anonymous

That would be 315 degrees.

- anonymous

ummm sqrt 3/2 , -1/2

- anonymous

yes. sqrt(3)/2, -1/2

- anonymous

Okay. You should know that Cosx= x

- anonymous

So what is the value for Cos330?

- anonymous

I got -.991...

- anonymous

Keep this exact. You just gave me the coordinates. and I just told you CosƟ=x

- anonymous

so what is the exact answer?

- anonymous

hint: (x,y)

- anonymous

Use the coordinates you gave me.

- anonymous

sqrt 3/2 , -1/2

- anonymous

Yes and I told you cosƟ=x so what is cos330?

- anonymous

I don't get it /.\ I'm sorry

- anonymous

when I plug in Cos330 it gives me the decimal I gave you

- anonymous

|dw:1389757103607:dw|

- 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

ygarcia what calculator are you using btw?

- anonymous

I don't have a calculator

- anonymous

Okay. Well just finish it. Cos330=A. What is A in that triangle? A for adjacent to theta.

- anonymous

-1/2?

- anonymous

|dw:1389757356882:dw|

- anonymous

No. Adjacent means next to. So what is next to theta that isn't the hypotenuse. -1/2 is opposite.

- anonymous

sqrt 3/2

- anonymous

There you go.

- anonymous

so the solution is sqrt 3/2?

- anonymous

cos330=Sqrt(3)/2

- anonymous

Yes

- anonymous

Now let's see if you learned anything.
Tell me the sin330 if you know that sinƟ=y

- anonymous

-1/2

- 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

So Cos= x value
and Sin= y value?

- anonymous

In reference to the circle

- 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

Okay, Thanks SO MUCH!!!! I don't fully get it yet but what you explained to me helped A LOT :)

- anonymous

You're welcome.

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