Polar Coordinates (AQA A-Level Further Maths): Flashcards

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Polar Coordinates
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Polar coordinates describe a point using

Distance from pole and angle from initial line

The pole in polar coordinates

Fixed reference point (equivalent to origin)

rr in polar coordinates

Distance from the pole to the point

θ\theta in polar coordinates

Angle from initial line, counterclockwise

Convert polar to Cartesian: x=x =

x=rcosθx = r\cos\theta

Convert polar to Cartesian: y=y =

y=rsinθy = r\sin\theta

Convert Cartesian to polar: r2=r^2 =

r2=x2+y2r^2 = x^2 + y^2

Convert Cartesian to polar: tanθ=\tan\theta =

tanθ=yx\tan\theta = \frac{y}{x}

Same point in polar coordinates can be represented how?

In infinitely many different ways

Polar equation r=ar = a (constant) represents

Circle of radius aa at the pole

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