Pre calculus Mrs. Spatola
Lesson #8 Name:
Objective: · solve real-world applications using trigonometric functions
(1) In physics class, Elena noticed the pattern shown in the accompanying diagram on an oscilloscope.
Which equation best represents the pattern shown on this oscilloscope?
(1) y = sin(½ x) + 1 / (3) y = 2 sin x + 1(2) y = sin x + 1 / (4) y = 2sin(-½ x) + 1
(2) A student attaches one end of a rope to a wall at a fixed point 3 feet above the ground, as shown in the accompanying diagram, and moves the other end of the rope up and down, producing a wave described by the equation y = a sin bx + c. The range of the rope’s height above the ground is between 1 and 5 feet. The period of the wave is 4p. Write the equation that represents this wave.
(3) A radio wave has an amplitude of 3 and a wavelength (period) of p meters. On the accompanying grid, using the interval 0p to 2p, draw a possible sine curve for this wave that passes through the origin.
(4) On the accompanying grid, graph the equations y = 4 cos x and y = 2 in the domain –p ≤ x ≤ p. Express, in terms of p, the interval for which 4 cos x ≥ 2.
(5) A pair of figure skaters graphed part of their routine on a grid. The male skater’s path is represented by the equation m(x) = 3 sin ½ x, and the female skater’s path is represented by the equation f(x) = -2 cos x. On the accompanying grid, sketch both paths and state how many times the paths of the skaters intersect between x = 0 and x = 4p.
(6) The tide at a boat dock can be modeled by the equation , where t is the number of hours past noon and y is the height of the tide, in feet. For how many hours between t = 0 and t = 12 is the tide at least 7 feet?
[Use the accompanying grid to graph the above equation and answer the question.]
(7) The average annual snowfall in a certain region is modeled by the function , where S represents the annual snowfall, in inches, and t represents the number of years since 1970.
(a) What is the minimum annual snowfall, in inches, for this region?
(b) In which years between 1970 and 2000 did the minimum amount of snow fall?
[Use the accompanying grid to graph the above equation and answer the questions.]