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Math Help - Intersection of Polar Curves

  1. #1
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    Intersection of Polar Curves

    Hello guys!

    I'm trying to brush up on my calc. 2.
    So I had two questions, find the points of intersections of both;

    33) r = 2sin(theta)

    r = 2sin(2theta)
    I get to sin(theta)/sin(2theta)=1
    what do I do with the "sin(2theta)."(Can this 2 be moved out?)
    Answer: (0,0), (3^1/2, pi/3), (-(3^1/2), pi/3)

    37) r=1
    r^2 = 2sin(2theta)
    Don't know what to do here...
    1 = +/- 2sin(2theta)
    ...?
    Answer: (1, pi/12), (1, 5pi/12), (1, 13pi/12), (1, 17pi/12)
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  2. #2
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    Quote Originally Posted by aeubz View Post
    Hello guys!

    I'm trying to brush up on my calc. 2.
    So I had two questions, find the points of intersections of both;

    33) r = 2sin(theta)

    r = 2sin(2theta)
    I get to sin(theta)/sin(2theta)=1
    what do I do with the "sin(2theta)."(Can this 2 be moved out?)
    Answer: (0,0), (3^1/2, pi/3), (-(3^1/2), pi/3)

    37) r=1
    r^2 = 2sin(2theta)
    Don't know what to do here...
    1 = +/- 2sin(2theta)
    ...?
    Answer: (1, pi/12), (1, 5pi/12), (1, 13pi/12), (1, 17pi/12)
    General advice not necessarily related to the above questions: It's always wise to draw the curves as well as do the algebra because the algebra doesn't always give all intersection points.

    Both problems assume that you have sufficient understanding of trigonometric functions to solve trigonmetric equations. (This would be an assumed prerequisite).

    33) 2 \sin (\theta) = 2 \sin (2 \theta)

    \Rightarrow 2 \sin (\theta) = 4 \sin (\theta) \cos (\theta)

    \Rightarrow 2 \sin (\theta) [1 - 2 \cos (\theta)] = 0

    \Rightarrow \sin (\theta) = 0 or \cos (\theta) = \frac{1}{2}.


    37) Solve 1 = 2 \sin (2 \theta) \Rightarrow \sin (2 \theta) = \frac{1}{2}.
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