Polar Coordinates (Edexcel A-Level Further Mathematics): Quizzes

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Polar Coordinates
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In polar coordinates, what does rr represent?

Distance from the pole

Which formula converts polar to Cartesian for xx?

x=rcos⁡θx = r \cos \theta

Convert Cartesian (3,3)(3, 3) to polar. What is rr?

323\sqrt{2}

What curve does r=ar = a represent?

Circle of radius aa at pole

What shape is the curve r=a(1+cos⁡θ)r = a(1 + \cos \theta)?

Heart-shaped (cardioid)

For rose curve r=acos⁡nθr = a \cos n\theta, how many petals if nn is odd?

nn petals

What shape does r2=a2cos⁡2θr^2 = a^2 \cos 2\theta produce?

Figure-eight (lemniscate)

How does the spiral r=kθr = k\theta behave as θ\theta increases?

Expands outward

For r2=f(θ)r^2 = f(\theta), what common mistake should be avoided?

Forgetting ±\pm roots

For r=2+2cos⁡θr = 2 + 2\cos\theta, what is rr when θ=π\theta = \pi?

00

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