Polar and Cartesian coordinates

Polar and Cartesian coordinates Quiz

Spec G1 · AQA A-Level Further Maths: Quiz

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  1. 1. Convert (−1,1)(-1,1) to polar coordinates with r>0r>0 and −π<θ≤π-\pi<\theta\le\pi.

    • A. (2,π4)\left(\sqrt2,\frac{\pi}{4}\right)
    • B. (2,3π4)\left(\sqrt2,\frac{3\pi}{4}\right)
    • C. (2,3π4)\left(2,\frac{3\pi}{4}\right)
    • D. (2,−π4)\left(\sqrt2,-\frac{\pi}{4}\right)

  2. 2. Convert (3,π2)\left(3,\frac{\pi}{2}\right) to Cartesian coordinates.

    • A. (3,0)(3,0)
    • B. (0,−3)(0,-3)
    • C. (3,3)(3,3)
    • D. (0,3)(0,3)

  3. 3. Find the Cartesian equation of r=2sin⁡θr=2\sin\theta.

    • A. x2+y2=2yx^2+y^2=2y
    • B. x2+y2=2xx^2+y^2=2x
    • C. y=2xy=2x
    • D. x2+y2=4x^2+y^2=4

  4. 4. Find the polar equation of the line x=3x=3.

    • A. r=3sin⁡θr=3\sin\theta
    • B. r=3r=3
    • C. rcos⁡θ=3r\cos\theta=3
    • D. rsin⁡θ=3r\sin\theta=3

  5. 5. Convert (−2,−2)(-2,-2) to polar form with r>0r>0 and −π<θ≤π-\pi<\theta\le\pi.

    • A. (22,−3π4)\left(2\sqrt2,-\frac{3\pi}{4}\right)
    • B. (22,π4)\left(2\sqrt2,\frac{\pi}{4}\right)
    • C. (22,3π4)\left(2\sqrt2,\frac{3\pi}{4}\right)
    • D. (8,−3π4)\left(8,-\frac{3\pi}{4}\right)

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