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Math Help - depressed by degrees problem

  1. #1
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    depressed by degrees problem

    Hi, I am a complete green horn on trig and have bought a rather naff "Trigonometry for Dummies" book that is beyond me.

    I do not accept I cannot learn it as this book is not written in a way I can understand so have ordered another title.

    Anyway onto my problem!

    The coordinate plain is on the iPhone which is 320 * 460

    The circle centre (is this the origin) is 160, 230

    I use these equations to get my distance from centre and the degrees that this distance represents around the inside of the circle.

    kSlideCentreX = 160 and kSlideCentreY = 230

    Code:
    distanceFromCentre = sqrt(((currentPosition.x - kSlideCentreX ) * (currentPosition.x - kSlideCentreX)) - ((currentPosition.y - kSlideCentreY) * ( currentPosition.y - kSlideCentreY)));
    this is how I get the slope

    Code:
    slope = (kSlideCentreY - currentPosition.y) / (kSlideCentreX - currentPosition.x);
    this gives me the radians

    Code:
    atan(slope)
    kRadiansPerDegree = 0.0174532f

    gives me the degrees ( but not fixed yet )

    Code:
    atan(slope) / kRadiansPerDegree
    this is supposed to fix them to real degrees?

    Code:
    90 - ( atan(slope) / kRadiansPerDegree)
    my problem is that any coords on the right of the circle run from 180 degrees at the top (12) to 0 at the bottom (6), and on the left side from 180 at the bottom (6) to 0 at the top (12).

    I can understand and learn things as long as they are done so in a fashion my brain can grasp

    I am searching and searching but coming up blank probably due to not asking the right question or how to phrase it.

    I would be very grateful if someone could point me in the right direction or if feeling very friendly and helpful tutor me through this problem so I can learn from it and expand?

    in hope......

    Thanks
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  2. #2
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    I am not sure what you're asking for. What is it you want to understand?.

    How to convert from radians to degrees?.
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  3. #3
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    Hi, well starting from 12 to 3 I would expect to see 0 to 90 then from 3 to 6 90 to 180 from 6 to 9 180 to 270 and finally from 9 to 12 270 to 360.

    But I get 180 to 90 to 0 to 90 to 180?

    I don't understand why this is so ?

    Tomorrow I am going to plot a circle on graph paper and draw a triangle in it to see if I can visualize the calculation of distance and subsequent angle to determine the degrees, but am struggling to understand.

    Have spent a lot of time tonight trying to find a downloadable trig course for beginners!
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  4. #4
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    In most applications the origin is the positive x-axis and travels counterclockwise. Therefore, as you have it in terms of a clock face.
    0 is at 3, 90 is at 12, 180 is at 9 and 270 is at 6. Then it goes around and 360 is at 3 again.

    The first quadrant is 0 to 90, second quadrant is 90 to 180, third quadrant is 180 to 270, fourth quadrant is 270 to 360(or 0).

    To find angles, use x=rcos{\theta} to find the x-coordinate

    y=rsin{\theta} to find the y-coordinate.

    r=\sqrt{x^{2}+y^{2}}, Pythagorean theorem.

    For instance, x=1 and y=1. r=\sqrt{1^{2}+1^{2}}=\sqrt{2}

    That is the length of the hypoteneuse of the triangle formed.

    Now, that is 45 degrees or \frac{\pi}{4} radians.

    x=\sqrt{2}sin(\frac{\pi}{4})=1, \;\ \sqrt{2}cos(\frac{\pi}{4})=1

    See?. We got the coordinates (1,1).

    This is a little different than the diagram because I used x and y of 1.

    If we use r=1 as in the unit circle, then x=1\cdot sin(\frac{\pi}{4})=\frac{\sqrt{2}}{2}. Just as on the diagram.

    Also, y=1\cdot cos(\frac{\pi}{4})=\frac{\sqrt{2}}{2}.

    To convert from radians to degrees, multiply by \frac{180}{\pi}

    To convert from degrees to radians, multiply by \frac{\pi}{180}

    I have posted a diagram of the unit circle so you can see. Those Books for Dummies are not the best to learn from.

    Does that help a wee bit?.
    Attached Thumbnails Attached Thumbnails depressed by degrees problem-unit_circle-small-.gif  
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  5. #5
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    Yep it does help a see bit.

    I understand the layout of the degrees and yep sure did drop the ball on that one LOL

    I lost you on the finding the x a y equations but caught up again on the conversion to degrees from radians.

    I would already have the x,y coords and would use the 3,4,5 rule to get the distance and use that for getting the degrees I think?

    Do you know if the product at top of this page Trigonometry Solved would be of any help to me? I know jack about trig but must learn it fast for work!

    Am trying to find. Course or book aimed at kids I suppose seeing as my knowledge of this is so poor!

    Example I only found out tonight that sine = opposite / hyp!

    See how little I know ?
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  6. #6
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    Am just Reading an interesting web site on unit circle!

    As I did not know what this was either
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  7. #7
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    There are all sorts of things if you google.

    We all have to start somewhere. I learned trig years back when I began surveying.

    Here is a diagram of the triangle with its respective trig and what sides they represent.

    Of course, if it is not a right triangle, then it gets more complicated.

    Law of Sines, Law of Cosines and so forth come into play. Lots to learn.
    Attached Thumbnails Attached Thumbnails depressed by degrees problem-angles.gif  
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  8. #8
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    Could someone confirm my thoughts that the example I have seen is wrong hence my confusion please?

    OK...I am told of a right triangle with a 30 degree angle an opposite length of 4 and an unknown hypotenuse.

    so to find the length hypotenuse, lets call it 'a' the following applies:

    sin x = opposite / hypotenuse

    sin 30 = 4 / a

    a sin 30 = 4

    a = 4 / sin 30

    4 sin 30 = 8

    Now I understand sin 30 = 0.5 so applying this to the above we get

    0.5 = 4 / a ( a is 8 )

    a 0.5 = 4 ( a is 8 )

    a = 4 / 0.5 ( a is 8 )

    4 0.5 = 8 ( no it does not? 4 0.5 = 2)

    Have I missed something or is this last line an incorrect example?
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