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51assign2

# 51assign2 - 2500-meter ride 2(4 points Find the amplitude...

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Math 51: Assignment 2 (25 points) Due by the time you take Exam II – Late Assignments will not be accepted . This assignment has 2 pages Do all work on a separate sheet of paper. You must show work to receive credit. Turn in work in order (#2 should come after #1, etc.) You may work in groups of up to 3 people. Points will be taken off, if more than 3 names are on one assignment. 1. (5 points) A bicycle has two sprockets, connected by the chain. The back tire of the bicycle is rotated by the rotation of the smaller sprocket. The bigger sprocket has a radius of 20 cm and the smaller has a radius of 8 cm; the bicycle tire has a radius of 40cm. The cyclist travels 2500 meters in 5 minutes. a. Find the linear and angular velocity of the tire. b. Find the linear and angular velocity of the small sprocket. c. Find the linear and angular velocity of the large sprocket. d. How many rotations does the rider pedal (which is attached to the large sprocket) on the

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Unformatted text preview: 2500-meter ride? 2. (4 points) Find the amplitude, period, phase shift (and the direction) and vertical shift of the following: a. y = 7 − 3cos 3 x + 2 π ( ) b. y = − 9csc 5 x − 7 ( ) + 3. (2 points) Sketch a graph of the damped harmonic function: y = 3 − t 5 sin 2 3 t 4. (3 points) Suppose csc α = − 3 and tan > . Find sin − ( ) , cos − ( ) and tan − ( ) . 5. (4 points) If sec = − 3 where 2 ≤ < and tan β = 3 where ≤ < 3 2 . a. Find sin + ( ) , cos − ( ) and tan + ( ) b. What quadrant is + ( ) in? 6. (4 points) Verify the following identities: a. sin 2 A − sin 2 B = cos 2 B − cos 2 A b. sin x + y ( ) cos x cos y = tan x + tan y 7. (4 points) Find a possible equation for each of the following graphs: a. b....
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