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Precalculus Trigonometry

  1. Jun 7, 2005 #1
    Can someone break down in "baby steps" how to solve the following?:

    cos7pi/6=?

    thank you. :uhh:
     
  2. jcsd
  3. Jun 7, 2005 #2
    You can either use the CAST quadrant diagram or the cos(A+B) formulae, but both rely on you knowing cos(pi/6)=(rt3)/2
     
  4. Jun 7, 2005 #3
    Q. How many times does pi go into a circle?
    A. Two times. And that is the same as going 360 degress.

    Q. Then half a circle is has one pi?
    A. Right.

    Q. So pi is like 180 degrees?
    A. Right, and Cos of 180 degress is Cos 6pi/6. And that is like having a trinangle that has no opposite edge. Such a triangle is not much of a triangle, O / H is zero.

    Q. So what is Cos 6pi/6?
    A. It is A/H where A and H are the same lenght, only we are going in a negative direction for A (relative to the X axis).

    Q. That means Cos 6pi/6 is -1?
    A. That's right.

    Q. Okay, that takes care of Cos 6pi/6, what about Cos 7pi/6?
    A. Well, that's like going 1/6th of pi (where pi is 180 degrees) farther than we already have. We've gone 6pi/6 to sweep half a circle, now we go a little more beyond that.

    Q. So that would be 30 degrees more, right?
    A. Right, becasue six times 30 is 180, and we want 1/6th more of that; so we go the extra 30 degrees to make 7/6th of pi.

    Q. So we are talking about a triangle with a 30 degree angle?
    A. That's right, and it is drawn along the negative x axis below it.

    Q. So how do I find Cos 30 degrees?
    A. You can draw a 30 degree triangle with a protractor and measure the ratio of A/H.

    Q. So will it be positive or negative?
    A. Even though it is a 30 dgree triangle, it has been layed along the X axis on the negative side. So A will be negative in the A/H ratio.
     
  5. Jun 7, 2005 #4

    mathwonk

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    look at a circle. and find 7pi/6. then ask what the coordinates of that point are.
     
  6. Jun 8, 2005 #5

    VietDao29

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    Why don't you use:
    [tex]\cos(\pi + \alpha) = -\cos{\alpha}[/tex]
    Viet Dao,
     
    Last edited: Jun 8, 2005
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