4. Consider the polar curves C₁ r = 2 sin 0 and C₂ = 2 cos 0, where 0 ≤ 0 ≤ 2π. a) Find the Cartesian equations of C₁ and C2 and make a neat sketch of these curves. b) Using polar equations of C₁ and C₂ to find their intersection points (Do not use their Cartesian equations!). c) Using polar equations of C₁ and C₂ to show that they intersect each other at right angles (Do not use their Cartesian equations!).

Q: Find the intersections and symmetry for the polar equation r sine = 1 and then draw it.

A: Any point on the polar coordinate system is represented by the ordered pair: r, θ. For a equation of…

Q: Plot the point having the polar coordinates ​(2​,30°​). Then find different polar coordinates…

A: (a) r<0, 0°≤θ<360° Given (r, θ)=(2, 30°) Coordinates will be x=r cosθ, y=r sinθ ⇒x=-2cos30°,…

Q: The Cartesian coordinates of a point are given. (a)     (−9, 9)   (i) Find polar coordinates  (r,…

A:

Q: Convert the polar coordinates (-8, 2π/3) into rectangular coordinates. Convert the rectangular…

A:

Q: 10. Sketch the curve of the polar equation r = 2 sin 0 . Find a rectangular equation for this curve.

A: