Finding points by distance and angle

Mathematics · Geometry · ages 17-18

Name ______________________ Date ____________

The point (6, 180 degrees) in polar form. What is its x-coordinate?
Answer: ______________
The point (2, 90 degrees) in polar form. What are its Cartesian coordinates?
- (0, 2)
- (2, 0)
- (0, -2)
- (-2, 0)
The point (2, 90 degrees) in polar form. What are its Cartesian coordinates?
- (0, 2)
- (2, 0)
- (0, -2)
The polar equation r equals 2. What shape is its graph?
- A spiral
- A straight line
- A circle
Which curve is simplest in polar form?
- y equals 2x plus 1
- r equals 5
- y equals x squared
Which curve is simplest in polar form?
- r = 5
- y = 2x + 1
- y = x^2
- (x - 4)^2 + y^2 = 9
The polar equation r = theta, with theta >= 0. What shape is its graph?
- A spiral
- A circle
- A parabola
- A straight line
The polar equation r equals theta, with theta from zero upward. What shape is its graph?
- A circle
- A parabola
- A spiral
The point (3, 4) in Cartesian form. What is its radius r in polar form?
Answer: ______________
x squared plus y squared equals 25 becomes what in polar form?
- r equals 25
- r equals 5
- theta equals 5

Answer key

For grown-ups. Fold this page away before handing over the rest.

-6 · x = 6 cos 180 = 6 by -1 = -6.
(0, 2) · x = 2 cos 90 = 0 and y = 2 sin 90 = 2.
(0, 2) · x equals 2 cos 90, which is 0, and y equals 2 sin 90, which is 2.
A circle · A fixed radius with a free angle traces a circle centred at the origin.
r equals 5 · r equals 5 is already a centred circle, while the line and parabola turn clumsy.
r = 5 · r = 5 is already a centred circle; the shifted circle and the line both turn clumsy in polar form.
A spiral · Radius grows steadily as the angle turns, winding outward forever.
A spiral · The radius grows steadily as the angle turns, winding outward forever.
5 · r squared equals 9 plus 16, which is 25, so r equals 5.
r equals 5 · Replace the sum with r squared to get r squared equals 25, so r equals 5.