Polar Coordinates — Drills
Polar Coordinates has 5 drill skills. Each one generates fresh questions every time, with a hint and full worked steps, so you can keep practising a single skill until it settles.
What these drills cover
These questions use 7 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Radius — Centre to edge. Half the diameter.
- Parabola — The U-shaped graph of a quadratic function.
- Ray — One endpoint and everything beyond it in one direction. Written AB.
- Complex number — Anything of the form a + bi, with a the real part and b the imaginary part.
- Complex plane — The plane where the horizontal axis is real and the vertical axis imaginary.
- Rectangular form — The ordinary (x, y) description.
- Quadrant — One of the four regions the axes divide the plane into.
Topolar
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Find r for the point (-7, 24).
Worked answer
25
√49+576 = 25
Problem 2
Find r for the point (3, -4).
Worked answer
5
√9+16 = 5
Torect
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Convert (4, 90°) to rectangular form. Give y.
Worked answer
4
4sin 90° = 4
Problem 2
Convert (8, 60°) to rectangular form. Give x.
Worked answer
4
8cos 60° = 4
Quadrants
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
For the point (-6, -6), find θ in degrees with 0° ≤ θ < 360°.
Worked answer
225
The reference angle is 45°
Quadrant III, so θ = 225°
Problem 2
For the point (-8, 8), find θ in degrees with 0° ≤ θ < 360°.
Worked answer
135
The reference angle is 45°
Quadrant II, so θ = 135°
Coterminal
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Give the angle between 0° and 360° naming the same direction as 656°.
Worked answer
296
656 - 360 = 296
Problem 2
Give the angle between 0° and 360° naming the same direction as 396°.
Worked answer
36
396 - 360 = 36
Modulus
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Find |z| for the complex number z = 7 + 24i.
Worked answer
25
√49+576 = 25
Problem 2
Find |z| for the complex number z = 3 - 4i.
Worked answer
5
√9+16 = 5