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Angular and Linear Velocity Calculations for Exercise Bike and Trig Functions Applications

This homework assignment focuses on understanding angular and linear velocity through real-life applications involving an exercise bike. Students must calculate the angular speeds of the bike's wheels and sprockets based on given diameters and speeds. Additionally, there are questions involving the length of a belt connecting two wheels, and applications of trigonometric functions for finding the volume of a cylinder inscribed in a sphere. The assignment also includes verifying trigonometric identities and writing algebraic expressions using inverse trigonometric functions.

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Angular and Linear Velocity Calculations for Exercise Bike and Trig Functions Applications

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  1. Pg. 395 Homework • Pg. 395 #57 – 60Study for Trig Mem Quiz on Friday!! • #47 #48 • #49 #50

  2. Angular and Linear Velocity! • Elena can now reach 48 mph on her new exercise bike in high gear. These bike wheels are 25 in. in diameter, the pedal sprocket is 12 in. in diameter, and the wheel sprocket is 4 in. in diameter (in high gear). Find the angular speed of the wheel and of both sprockets in rad./hr.

  3. Belt Length! • If r1 = 18in. And r2 = 11 in. and the centers of the wheels are 36 in. apart, find the length of the belt.

  4. Applications of Trig Functions • A right circular cylinder is inscribed in a sphere of radius 20. Find a complete graph of the situation for the volume V of the cylinder in terms of the angle Ɵ. Find the dimensions of the cylindrical of maximum volume that can be inscribed in the sphere.

  5. Inverse Trig Functions Evaluating a Trig Expression Verifying an Identity Show that:sin-1x + cos-1x = π/2 for all x in [-1, 1]. • Write an algebraic expression in terms of v for sin(sin-1v) and cos(tan-1v).

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