Question

1. A pendulum is connected to a rope 3m long, which is connected to a ceiling 4m high. The angle between its widest swing and vertical hanging position is pi/3. If the pendulum swings out to its widest position for 2 seconds, model the horizontal displacement of the pendulum using a sine function, considering vertical to be x=0.

2. The tides at Cape Capstan change the depth of the water in the harbour. On one day in September, the tides have a high point of approximately 13m at 3pm and 1.6m at 9pm. The sailboat has a draft of 2.5m deep. The captain of the sailboat plans to exit the harbourer at 8:30pm.
a. Write a cosine trigonometric equation that represents the situation described.
b. Plot an accurate graph 1 cycle.
c. Determine whether the sailboat can exit the harbour safely.

3. The average number of customers, c, at a 24-hour sandwich shop per hour is modelled roughly by the equation c(h)=-5cos[pih/12]+12, with h=0 representing midnight.
a. How many hours per day are there 13 customers per hour, to the nearest hour?
b. What is the maximum number of customers?
c. What time of day is peak(max) business?

4. A 3m ladder is leaning against a vertical wall such that the angle between the ground and the ladder is pi/3. What is the exact height that the ladder reaches up the wall?

Please show all the work. Please and thanks.

Answer 1

That's two lengthy problem sets you have dumped on us, with no indication of effort on your part. Whassup with that?
#1. the amplitude is 3cos(π)
the period is 4*2 = 8
x(0) = 0
See what you can do with that.

#2. follow steps similar to #1
#3. (a) solve -5cos[pih/12]+12 >= 13
(b) use the amplitude
(c) when is cos a minimum?

#4. Draw a diagram and review your basic trig functions.
h/3 = sin(pi/3)

Answer 2

I was given those questions and I do not understand them myself.