Polar Graphing Worksheets Grade 12

1. ∫(x³ - 2x² + 5) dx from -1 to 2 = ?
2. ∫(x² + 2x - 3) dx from 1 to 4 = ?
3. Liam is designing a roller coaster that follows a polar curve. The track's path is given by r(θ) = 4cos(3θ) where r is in meters. He needs to install safety barriers at all points where the track is exactly 2 meters from the center pole. Determine all angles θ in the interval [0, 2π) where this occurs.

…and 5 more problems

1. Graph r = 4cos(2θ) and identify the shape.
2. Graph r = 5 + 5cos(θ). Identify the shape and find the maximum value of r.
3. Find the area enclosed by the polar curve r = 4sin(3θ) in the first quadrant. Express your answer as a simplified multiple of π.

…and 6 more problems

1. Graph r = 5 + 5cosθ and identify the shape.
2. An astronomer is tracking a comet's path through the solar system using polar coordinates. The comet's trajectory follows the polar equation r = 3/(1 + 2cosθ). Determine the eccentricity of this conic section and identify what type of orbit the comet has.
3. Graph r = 6 + 6cos(θ) and identify the shape.

…and 5 more problems