Sinusoidal functions assignment KEY
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Nov 24, 2024
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Math 30-1
Name _____________________
Sinusoidal Functions Assignment
1.
Due to the tidal variations, the depth of water in a harbour is given by the formula
where D is the depth of water in metres and t is the time in hours after midnight on Monday night.
a)
What were the greatest and least depths of water in the harbour? 2 m minimum depth, 10 m maximum depth
b)
At what time was low tide on Tuesday morning?
2:15 AM
c)
A boat needs at least 4 metres of water to leave the harbour. Can the boat leave the harbour at 3:00 p.m. Tuesday? Justify your answer.
No. the depth of the water in the harbor at that time would only be 3.23 m.
2.
Write a sine and cosine equation for the sinusoidal function shown below.
Y=20 sin (
/20(
π
t - 25)) + 30 OR Y=20 sin (
/20(
π
t + 15)) + 30
Y = 20 cos (
/20(
π
t - 35)) + 30 OR Y = 20 cos (
/20(
π
t + 5)) + 30
3.
The graph below shows how the number of hours (h) of daylight in a European city changes during the year.
a) Mid-winter is the day with the least hours of daylight. How many hours of daylight will there be on mid-winter's day?
9.33 h or 9h20min
b) How many days after April 21
st
will mid-winter occur?
274 days
4.
A Ferris wheel ride can be represented by a sinusoidal function. A Ferris wheel at Westworld Theme Park has a radius of 15 m and travels at a rate of 6 rev/min in a clockwise rotation. You and your friend board the ride at the bottom chair from a platform one meter above the ground.
a)
Sketch a sinusoidal graph to represent the Ferris wheel ride. Label the axes and use appropriate scales.
b)
Write the cosine equation to represent this function.
Y = 15 cos ( /5(
π
t – 5)) +16
c)
If the Ferris wheel does not stop, determine the height you and your friend are above the ground after 28 seconds. Round your answer to the nearest tenth.
11.4 m (use trace x=28)
31
Height (m)
1
10
Time (sec)
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