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    The question is:
    3) The polar equation of a curve is rcos(?/2) = a for -pi<?<pi
    (i) show that rsin? may be expressed as 2a(sin(?/2)) and deduce that as ? tends to pi, the curve approaches the lines with cartesian equations y=+/- 2a

    so I just used double angle formulas with a bit of re-arranging, wasn't that hard, then putting pi as ? gets you to y=+/- 2a as rsin? is an expression for a y coordinate.

    (ii) Sketch the curve. I have no idea how to do this. I don't even know what the expression rcos(?/2) = a is meant to represent, but I rearraged it to get r=a(sec(?/2). Then plotted r(t)=(sec(?/2) on this site:

    http://www.calculator-grapher.com/gr...alculator.html

    And got pretty much a straight line through 1, although not quite.
    Is this correct? Am I doing something wrong?

    (iii) Calculate the area of the sector of the curve between theta = plus or minus half pi.

    No idea either.... I suck at this chapter.

    Thanks for any help ;>

    Also how do I prove that arcsinhx = ln(x+sqrt(x^2 +1) from the starting definition of sinhx = 1/2(e^x +e^-x)
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    (Original post by jamie092)
    The question is:
    3) The polar equation of a curve is rcos(?/2) = a for -pi<?<pi
    (i) show that rsin? may be expressed as 2a(sin(?/2)) and deduce that as ? tends to pi, the curve approaches the lines with cartesian equations y=+/- 2a

    so I just used double angle formulas with a bit of re-arranging, wasn't that hard, then putting pi as ? gets you to y=+/- 2a as rsin? is an expression for a y coordinate.

    (ii) Sketch the curve. I have no idea how to do this. I don't even know what the expression rcos(?/2) = a is meant to represent, but I rearraged it to get r=a(sec(?/2). Then plotted r(t)=(sec(?/2) on this site:

    http://www.calculator-grapher.com/gr...alculator.html

    And got pretty much a straight line through 1, although not quite.
    Is this correct? Am I doing something wrong?
    Correct if a=1/2
    (iii) Calculate the area of the sector of the curve between theta = plus or minus half pi.

    No idea either.... I suck at this chapter.

    Thanks for any help ;>
    THE area of sector A=\int^{\beta}_{\alpha} r^2(\theta)\ d\theta
    Also how do I prove that arcsinhx = ln(x+sqrt(x^2 +1) from the starting definition of sinhx = 1/2(e^x +e^-x)
    y=1/2(e^x+e^-x)
    Changing x with y
    x=1/2(e^y+e^-y) and solve this to y (=arsinhx)
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    thanks so much <3
 
 
 
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