Question

1.Find a possible formula for the trigonometric function whose values are in the following table.

x	0	2	4	6	8	10	12
y	-2	-5	-2	1	-2	-5	-2

y=

2. A population of rabbits oscillates 21 above and below an average of 103 during the year, hitting the lowest value in January (t = 0). Find an equation for the population, P, in terms of the months since January, t.

P(t) =

What if the lowest value of the rabbit population occurred in April instead?

P(t) =

3. A Ferris wheel is 20 meters in diameter and boarded from a platform that is 4 meters above the ground. The six o'clock position on the Ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 2 minutes. How many minutes of the ride is spent higher than 20 meters above the ground?

4. Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the temperature varies between 52 and 88 degrees during the day and the average daily temperature first occurs at 8 AM. How many hours after midnight, to two decimal places, does the temperature first reach 65 degrees?

Answer 1

Doubt or problem in this then comment below.. i will help you..

by rules and regulation we allow to do only one problem at a time . here i solve 2 problems .

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1..

timeperiod = 2pi/(8-0) = 2pi/8

oscillate about level = (-5+1)/2 = -2

amplitude = 3

so ,

y = - 2 - 3 sin(2 pi x/8)  

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4...

average temper = 70

ampltiude = 18

period = 2pi/24

so , y = 70 + 18 sin(2pi(x-8)/24)

y = 65  

gives us x = 6.925

answer = 6.93