ANIMATIONS FOR TRIGONOMETRY

ANIMATIONS FOR TRIGONOMETRY

	Terrific Sine Cosine Animation relating the graphs to the definitions of the functions on the unit circle by XIAO Gang. Check it out.
	My Own Sine Animation
	My Own Sine-Cosine Animation
	My Pretty Sine-Cosine Animation
	Another Pretty Sine-Cosine Animation This one should be opened in Quicktime. QuickTime 6 free download.

Ferris Wheel Problem

A circular Ferris wheel has a radius of 20 feet. The center of the Ferris wheel is 26 feet above the ground. There is one hanging seat hooked up and this seat always hangs straight down 4 feet from a point on the circumference of the Ferris wheel. When running the Ferris wheel makes one revolution every 20 seconds and turns counterclockwise. Construct a position function for the point at the bottom of the hanging seat (the point always 4 feet directly below a point on the circumference of the Ferris wheel). In doing this assume the Ferris wheel reaches full speed in less than 1/4 revolution and model your position function such that the point on the circumference of the Ferris wheel directly above the hanging seat is at three o'clock at time t = 0. From your position function find a velocity function for the point on the bottom of the hanging seat. With the Ferris wheel at full speed, find the magnitude of the velocity of the point on the bottom of the hanging seat 5/3 seconds after it reaches its lowest point. What is its lowest point? Click here to see an animation.

A bird is perched at the top of a pole that is 10 feet high. It flies in an elliptical path to the top of a pole that is 30 feet high and 50 feet away from the 10 foot pole. The center of the elliptical path is directly above the 10 feet pole and at the same height as the 30 foot pole. It takes the bird 10 seconds to fly from the top of the 10 foot pole to the top of the 30 foot pole. Give a parametric representation of the path of the bird where t = 0 represents the time when the bird leaves the 10 foot pole. Click here to see an animation of the bird's flight from pole to pole.

DANCING CIRCLES

DANCE LINE OF CIRCLES

Dancing Circles is an animation consisting of eight small circles traveling around the four limacons pictured below, two circles traveling on each limacon. The centers of the circles follow the paths given parametrically at the right. The centers always remain in a straight line. Dance Line of Circles is the same animation with the addition of the rotating straight line through the centers of the circles and also a small black circle at the origin that does not move

DANCING EYES

DANCING LIMACONS

To the left is the polar graph of r = 2 + 4sin(2t) - 4cos(2t).

Click the graph to see an animation.

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Lane Vosbury, Mathematics, Seminole State College email: vosburyl@seminolestate.edu