Workshop 7

# Workshop 7 - The function r = 1 sin can be graphed in the r...

This preview shows pages 1–2. Sign up to view the full content.

The function r = 1 - sin θ can be graphed in the r, θ plane to help graph the cardioid in the x, y plane. The graph of the function in the r, θ plane can be derived by evaluating 1 - sin θ for various θ ’s from 0 to 2 π . By seeing how 1-sin θ behaves in the r, θ plane, the function of 1-sin θ can be graphed in the x, y plane. To graph the cardioid, start from θ = 0 and plot increments of π /2 all the way to 2 π , which is derived from the graph above ( θ = 0, r = 1; θ = π /2, r = 0; θ = π , r = 0; θ = 3 π /2, r = 2; θ = 2 π , r = 1). Essentially, by making θ range from 0 to 2 π , it is possible to graph one period of r = 1 - sin θ , which can be derived from the graph in the x, y plane. In addition to graphing the points in increments of π /2, it must be observed that the r (of r = 1 - sin θ ) decreases from θ = 0 to θ = π /2, increases from θ = π /2 to θ = π , increases from θ = π to θ = 3 π /2, and then decreases from θ = 3 π /2 to θ = 2 π , to trace out the graph of the cardioid. Besides graphing the cardioid, the function r = 1 should be graphed; this function is just a circle with radius one, with the center at the origin, in the x, y plane. The first part of the problem requires finding what percent of the cardioids enclosed area lies above the x-axis. To do this the area of the cardioid from 0 to π (which lies above the x axis) must be divided by the entire area of the cardioid from 0 to 2

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 02/29/2012 for the course MATH 151 taught by Professor Sc during the Fall '08 term at Rutgers.

### Page1 / 3

Workshop 7 - The function r = 1 sin can be graphed in the r...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online