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HPC WB4.5 - Solve Trig Eqn 3

Last updated over 5 years ago

4 questions

1

Question 1

1.

During an experiment, the intensity i(t) of the electric current of a device as a function of time t elapsed since the beginning of the experiment is given by i(t)=6\sin\left( \frac{\pi t}{12}+\frac{2\pi}{3}\right)+6 where t is expressed in second. The device emits a sound signal each time the intensity is equal to 9.

a. How many sound signals does the device emit during the first 30 seconds?

b. What is the intensity at 45 seconds?

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Question 2

2.

The average temperature of a fictitious town is given by the equation f(x)=20\sin\left(\frac{\pi}{13}x\right)+2 where x represents the number of weeks since the beginning of the year.

a. During the course of the year, for how many weeks was the average temperature higher than 15\degree C?

b. What was the average temperature on week 12?

Question 3

3.

A pendulum on a gradfather clock is swinging back and forth as it keeps time. A device is measuring the height the pendulum is above the floor as it swings back and forth. This device is modeled by h(t)=12\sin\left(\pi t+\frac{\pi}{2}\right)+24 where t is in seconds and the height is in cm.

a. How many times is the height 14cm over the first minute?

b. What is the height at 37 seconds?

Question 4

4.

Jackie, Nicolle and Megan are playing skip rope. The rope height is modeled by h(t)=1.25\cos\left(\frac{\pi}{2}t-\frac{\pi}{2}\right)+1.5, where t is modeled by seconds and the height is measured by meters.

a. How many times is the rope 2 meters above the ground over the first minute?

b. What is the height at 43 seconds?