MAT112-03/04 Section 5.4 In Class Problems.

#6. Find the period and amplitude, then describe the viewing rectangle. y = 3/2 cos(p x/2).
Solution: amplitude = 3/2. period = 2p / b = 2p / (p / 2) = 4. Window: Xmin = -2p , Xmax = 2p , Xscl = p , Ymin = -2, Ymax = 2, Yscl = 1.

#10. y = 1/3 sin (8x)
Solution: amplitude = 1/3, period = 2p / 8.

#16. Describe the relationship between the graphs of f and g. f(x) = cos x, g(x) = cos (x + p ).

Solution: g is a shift of f p units to the left. Graph both functions in the same viewing window to verify this.

#18. Describe the relationship between the graphs of f and g. f(x) = sin (3x), g(x) = sin (-3x).

Solution: g is a reflection of f about the y-axis.

#26. Describe the relationship between the graphs of f and g.

Solution: Shift the graph of f two units up to obtain the graph of g.

#40. They are the same graph. So sin x = -cos (x + p / 2).

#83.

a.) Plot sin x and its polynomial approximation sin x » x - x³/3! + x⁵/5!.

b.) Plot cos x and its polynomial approximation cos x » 1 - x²/2! + x⁴/4!.

c.) Guess the next term in the approximations and plot these approximations.

#87. Daily fuel consumption, C = 30.3 + 21.6 sin (2p t / 365 + 10.9), where t is the time in days and t = 1 is Jan 1. What is the period of the model? Is this what is expected? Explain.

Solution: The period is 2p / b = 2p / (2p / 365) = 365. We would expect daily fuel comsumption on a farm to have a period of one year.

What is the average daily fuel consumption? Which term of the model did you use? Explain.

Solution: The sine wave model has been shifted up by 30..3. This is the average value of the function, 30.3 gallons per day.

Graph the model and approximate the time of the year when consumption exceeds 40 gallons per day.

Solution: 124 £ t £ 252.

Essential Trigonometry, Math Links

by Jack Tompkins