Sketch the region in the plane that represents r lt4 pi le

Question

On the graph below, do the following:

1. Plot the polar coordinates (2, π), (3,7π/4) and (-5,3π/2) below.

2. Sketch the region in the plane that represents r <4; π ≤ θ ≤ 2π on the grid below.

3. Sketch the curve for r² = cos 4θ. On the grid below.

4. Find the Cartesian formula for r = tan θ sec θ

5, sketch r² = sin 2θ and find the area it encloses.

6. Find the area of the region inside r = 1- sine θ and outside r = 1. Also sketch the curves.

7. Find the vertices, foci, and asymptotes of the hyperbola 2y²- 3x² - 4y +128 + 8 = 0; also sketch the graph.

8. Find the equation of an ellipse with foci (±1,2) and major axis 6.