Mid Chapter Review
Chapter
Chapter 6
Section
Mid Chapter Review
Solutions 5 Videos

Sketch the graph of a periodic function whose period is 10 and whose range is \{y\in \mathbb{R} \vert 4 \leq y\leq 10 \}

0.57mins
Q1

a. Graph the function g(x) = 5 \cos(2x) + 7without using a graphing device when 0^o \leq x \leq 360^o and 0 \leq g(x) \leq 15. Determine the period, equation of the axis, amplitude, and range of the function.

b. Explain why the function is sinusoidal.

c. Calculate g(125).

d. Determine the values of x, 0^o \leq x \leq 360^o, for which g(x) = 12.

3.02mins
Q3

Determine the coordinates of the new point after a rotation of 64° about (0, 0) from the point (7, 0).

1.29mins
Q4

Two white marks are made on a car tire by a parking meter inspector. One mark is made on the outer edge of the tire; the other mark is made a few centimetres from the edge. The two graphs show the relationship between the heights of the white marks above the ground in terms of time as the car moves forward.

a. What is the period of each function, and what does it represent in this situation?

b. What is the equation of the axis of each function, and what does it represent in this situation?

c. What is the amplitude of each function, and what does it represent in this situation?

d. Determine the range of each function.

e. Determine the speed of each mark, in centimetres per second.

f. If a third mark were placed on the tire but closer to the centre, how would the graph of this function compare with the other two graphs?

0.00mins
Q5

The position, P(d), of the Sun at sunset, in degrees north or south of due west, depends on the latitude and the day of the year, 51’. For a specific latitude, the position in terms of the day of the year can be modelled by the function

 \displaystyle P(d) = 28\sin(\frac{360}{365}d - 81)^o .

a. Graph without using a graphing device.

b. What is the period of the function, and what does it represent in this situation?

c. What is the equation ofthe axis ofthe funCtion, and what does it represent in this situation?

d. What is the amplitude of the function, and what does it represent in this situation.

e. Determine the range of the function.

f. What is the angle of sunset on February 15.