The polar system: check 1
Difficulty: ★★☆Info
Maths4U Original · Short practice
The closed polar curve is \(\displaystyle r=11(1+\frac{1}{4}\cos\theta)\) for \(0\le\theta\le2\pi\). Its radius is positive on this interval.
Find the maximum radius.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
The polar system: review variant 1
Difficulty: ★★☆Info
Maths4U Original · Short practice
The closed polar curve is \(\displaystyle r=12(1+\frac{1}{2}\cos\theta)\) for \(0\le\theta\le2\pi\). Its radius is positive on this interval.
Find the maximum radius.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
The polar system: check 2
Difficulty: ★★☆Info
Maths4U Original · Short practice
The closed polar curve is \(\displaystyle r=12(1+\frac{1}{2}\cos\theta)\) for \(0\le\theta\le2\pi\). Its radius is positive on this interval.
The enclosed area is Aπ. Find A.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
The polar system: review variant 2
Difficulty: ★★☆Info
Maths4U Original · Short practice
The closed polar curve is \(\displaystyle r=13(1+\frac{3}{4}\cos\theta)\) for \(0\le\theta\le2\pi\). Its radius is positive on this interval.
The enclosed area is Aπ. Find A.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
The polar system: check 3
Difficulty: ★★☆Info
Maths4U Original · Short practice
The closed polar curve is \(\displaystyle r=13(1+\frac{3}{4}\cos\theta)\) for \(0\le\theta\le2\pi\). Its radius is positive on this interval.
Find the tangent gradient at \(\displaystyle \theta = \frac{\pi }{2}\).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
The polar system: review variant 3
Difficulty: ★★☆Info
Maths4U Original · Short practice
The closed polar curve is \(\displaystyle r=14(1+\frac{1}{4}\cos\theta)\) for \(0\le\theta\le2\pi\). Its radius is positive on this interval.
Find the tangent gradient at \(\displaystyle \theta = \frac{\pi }{2}\).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
The polar system: check 4
Difficulty: ★★☆Info
Maths4U Original · Short practice
The closed polar curve is \(\displaystyle r=14(1+\frac{1}{4}\cos\theta)\) for \(0\le\theta\le2\pi\). Its radius is positive on this interval.
Find the y-coordinate at \(\displaystyle \theta = \frac{\pi }{2}\).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
The polar system: review variant 4
Difficulty: ★★☆Info
Maths4U Original · Short practice
The closed polar curve is \(\displaystyle r=15(1+\frac{1}{2}\cos\theta)\) for \(0\le\theta\le2\pi\). Its radius is positive on this interval.
Find the y-coordinate at \(\displaystyle \theta = \frac{\pi }{2}\).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.