40S Applied Math Mr. Knight – Killarney School Slide 1 Unit: Sinusoids Lesson: SIN-L5 Solving Sinusoid Problems Solving Sinusoid Problems Learning Outcome B-4 SIN-L5 Objectives: To solve problems involving sinusoidal data.

40S Applied Math Mr. Knight – Killarney School Slide 2 Unit: Sinusoids Lesson: SIN-L5 Solving Sinusoid Problems When solving problems that involve periodic (sinusoidal) function, a good procedure to follow is: Draw a rough graph by plotting the points and sketching a curve of best fit Write an algebraic equation that represents the sinusoidal graph. The equation should be in the form: y = a sin b(x + c) + d Use the equation to find any required values or information Intro – Solving Sinusoid Problems

40S Applied Math Mr. Knight – Killarney School Slide 3 Unit: Sinusoids Lesson: SIN-L5 Solving Sinusoid Problems A water wheel with a 7.0 ft radius has 1.0 ft. submerged in the water as shown, and rotates counterclockwise at 6.0 revolutions per minute. A bug is sitting on the wheel at point B. You start your stopwatch, and two seconds later the bug at point B is at its greatest height above the water. You are to model the distance h of the bug from the surface of the water in terms of the number of seconds t the stopwatch reads. Example 1

40S Applied Math Mr. Knight – Killarney School Slide 4 Unit: Sinusoids Lesson: SIN-L5 Solving Sinusoid Problems Example 1

40S Applied Math Mr. Knight – Killarney School Slide 5 Unit: Sinusoids Lesson: SIN-L5 Solving Sinusoid Problems The chart below shows Winnipeg's average monthly temperature Example 2

40S Applied Math Mr. Knight – Killarney School Slide 6 Unit: Sinusoids Lesson: SIN-L5 Solving Sinusoid Problems The chart below shows Winnipeg's average monthly temperature Example 2

40S Applied Math Mr. Knight – Killarney School Slide 7 Unit: Sinusoids Lesson: SIN-L5 Solving Sinusoid Problems The chart below shows Winnipeg's average monthly temperature Example 2

40S Applied Math Mr. Knight – Killarney School Slide 8 Unit: Sinusoids Lesson: SIN-L5 Solving Sinusoid Problems A spacecraft is in an elliptical orbit around the earth as shown in the diagram. At its perigee the spacecraft is at its lowest point above the earth's surface, and at its apogee it is at its highest point above the earth. The equation: describes the spacecraft's distance from the earth over time, where x represents the time in minutes, and y the distance in kilometres. Example 3

40S Applied Math Mr. Knight – Killarney School Slide 9 Unit: Sinusoids Lesson: SIN-L5 Solving Sinusoid Problems An electric heater cuts in and out on a cyclical basis as it heats the water in a hot tub. The water temperature C in degrees Celsius varies sinusoidally with time t. The thermostat is set to turn the heater on when the temperature drops to 36°C and off when it reaches 42°C. In order to measure the period, a timer was started at 0 when the heater cut in. The heater turned off 30 minutes later and turned on again after another 30 minutes. Example 4

40S Applied Math Mr. Knight – Killarney School Slide 10 Unit: Sinusoids Lesson: SIN-L5 Solving Sinusoid Problems An electric heater cuts in and out on a cyclical basis as it heats the water in a hot tub. The water temperature C in degrees Celsius varies sinusoidally with time t. The thermostat is set to turn the heater on when the temperature drops to 36°C and off when it reaches 42°C. In order to measure the period, a timer was started at 0 when the heater cut in. The heater turned off 30 minutes later and turned on again after another 30 minutes. Example 4