1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Science Advisor
    Homework Helper

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

    VietDao29

    User Avatar
    Homework Helper

    Why don't you use:
    [tex]\cos(\pi + \alpha) = -\cos{\alpha}[/tex]
    Viet Dao,
     
    Last edited: Jun 8, 2005
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Precalculus Trigonometry
  1. Precalculus Help (Replies: 3)

  2. PreCalculus Functions (Replies: 1)

Loading...