Converting between polar and rectangular coordinates practice problems
Between polar and rectangular: points both ways, and simple curves. 10 problems with worked solutions; in 10 of them every equation is proved by a computer algebra system.
Write the polar equation \( \displaystyle r^{2} \sin{\left(2 \theta \right)} = 4 \) in rectangular form.
Convert the polar point \( \displaystyle \left(5, \frac{\pi}{2}\right) \) to rectangular coordinates.
Convert the rectangular point \( \displaystyle \left(- 2 \sqrt{2}, - 2 \sqrt{2}\right) \) to polar coordinates with \( \displaystyle r > 0 \) and \( \displaystyle 0 \le \theta < 2\pi \).
Convert the rectangular point \( \displaystyle \left(0, 2\right) \) to polar coordinates with \( \displaystyle r > 0 \) and \( \displaystyle 0 \le \theta < 2\pi \).
Write the polar equation \( \displaystyle r \sin{\left(\theta \right)} = 4 \) in rectangular form.
Write the polar equation \( \displaystyle r = 2 \) in rectangular form.
Write the polar equation \( \displaystyle r = 8 \cos{\left(\theta \right)} \) in rectangular form.
Write the polar equation \( \displaystyle r = 12 \cos{\left(\theta \right)} \) in rectangular form.
Write the polar equation \( \displaystyle r = 2 \sin{\left(\theta \right)} \) in rectangular form.
Convert the polar point \( \displaystyle \left(2, 0\right) \) to rectangular coordinates.