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Math Help - finding the area(problem with secant)

  1. #1
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    finding the area(problem with secant)

    this is the last one i have left on my homework. Find the area of the region inside r = 10 and to the right of r = 6*sec(theta)

    i'm having problem graphing the last one because the sec of 90 is zero right? which is totally throwing off my graph. what do i do in this situation.
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  2. #2
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    Area in polar coordinates

    Hello tomobson
    Quote Originally Posted by tomobson View Post
    this is the last one i have left on my homework. Find the area of the region inside r = 10 and to the right of r = 6*sec(theta)

    i'm having problem graphing the last one because the sec of 90 is zero right? which is totally throwing off my graph. what do i do in this situation.
    No, it's \cos 90^o = 0.

    But what you want is this:

    r = 10 is a circle, centre O, radius 10.

    r = 6 \sec\theta is a straight line through through (6, 0) perpendicular to the initial line. (Check it out: draw this line, and join any point on it to O, and then look at the value of 6\sec\theta.)

    So you need the area of the segment of the circle radius 10, cut off by a chord that is 6 units from the centre of the circle. (You get a 6, 8, 10 triangle, so it's very easy!)

    Grandad
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