Radian trig graph word problems
- 1. RADIANTRIG GRAPHWORD PROBLEMS Goal: To solve word problems involving radian trig graph equations that model real-life phenomena.
- 2. #1 The tide at a boat dock can be modeled by the equation: 𝑦 = −2 cos 𝜋 6 𝑡 𝜋 + 8 where t is the number of hours past noon and y is the height of the tide in feet. How many hours between t = 0 and t = 12 is the tide at least 7 feet?
- 3. #2 The temperature in Syracuse varies throughout the year. A Sinusoidal equation provides a good model for the average temperature throughout the year. The equation: 𝑓 𝑡 = − 24.032 cos .503𝑡 + 47.364 represents the average temperature in Syracuse as a function of time, t in months. Note: t = 0 represents January 1st. What is the maximum temperature for the year? What is the minimum temperature for the year? What is the amplitude of the equation?
- 4. #3 The occurrence of sunspots during September can be modeled by the equation: 𝑦 = 44.2 sin 𝜋 7.8 (𝑥 − 2.9) + 148 in which x is the day of the month. What are the maximum number of sunspots that occurred in September? What are the minimum number of sunspots that occurred in September? What is the average value of sunspots that occurred in September? Notes: 30 days in September; Average = (max + min)/2
- 5. #4 The average annual snowfall in a certain region is modeled by the function 𝑆 𝑡 = 20 + 10 cos 𝜋 5 𝑡 where S represents the annual snowfall, in inches, and t represents the number of years since 1970. What is the minimum annual snowfall, in inches, for this region? In which years between 1970 and 2000 did the minimum amount of snow fall?
- 6. #5 A grandfather clock has a pendulum that moves from its central position according to the function 𝑃 𝑡 = −3.5 sin 𝜋 2 𝑡 where t represents time in seconds. How many seconds does it take the clock to complete one full cycle from center to the left then the right and then back to the center?
- 7. #6 The depth of the water on the shore of a beach varies as the tide moves in and out. The equation: 𝐷 𝑡 = .75 cos 𝜋 6 𝑡 + 1.5 models the depth of the water, D(t), in feet and t as time in hours. What is the amplitude of the equation? What is the period of the equation? In how many hours will the tide be at its lowest? How deep will the water be in 2 hours after the high tide? When will the water be 2 feet deep?