SOLUTION: 1) The height of a nail in a bicycle tire as it rotates around is periodic in nature. The radius of the tire is 30cm and at the current pedaling speed the tire rotates once ever

Question 1183665: 1) The height of a nail in a bicycle tire as it rotates around is periodic in
nature. The radius of the tire is 30cm and at the current pedaling speed the tire
rotates once every second.
a. Determine the equation of a sinusoidal function that models this situation
assuming that the nail starts on the ground at time zero.
b. At what time(s) during the first two seconds is the nail at a height of 30cm?
2) A swimmer on a floating air mattress will follow the rise and fall of the waves in the lake. When the person is on the top of the wave her feet are 1.5m above the average surface height of the lake. When she is in a trough her feet dig 0.5m into the water (-0.5m). The peaks of the waves are separated by two seconds. Create an equation of the sinusoidal function that models this movement assuming that she starts at the average surface height of the lake and heads upwards.
3) Prove the following trig identities:
a) tan 2x- 2tan 2x sin^2x= sin 2 x
b) sec^2x-2sec x cos x + cos^2x= tan^2x- sin^2 x
Answer by ikleyn(52925) (Show Source): You can put this solution on YOUR website!
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