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

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Polar Coordinates
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What is the pole in the polar coordinate system?

The fixed reference point

What does θ\theta represent in polar coordinates (r,θ)(r, \theta)?

Angle from initial line, anticlockwise

Which represents the same point as (2,π3)(2, \frac{\pi}{3})?

(2,4π3)(-2, \frac{4\pi}{3})

What conditions ensure unique polar representation?

r0r \geq 0 and π<θπ-\pi < \theta \leq \pi

What is the formula for xx when converting from polar to Cartesian?

x=rcosθx = r\cos\theta

What is the formula for rr when converting from Cartesian to polar?

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

What curve does the polar equation r=ar = a (constant) produce?

Circle of radius aa at the pole

What does θ=c\theta = c with r0r \geq 0 produce?

A half-line (ray) from the pole

How does the restriction r0r \geq 0 affect polar curves?

It can remove inner loops

Why is finding polar curve intersections challenging?

Coordinates are not unique

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