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Modeling with Sine Functions

Modeling with Sine Functions. Circular Motion. Linear speed Units are always length per time mph (bike or car speeds) Angular speed rpm (revolutions per minute) Engine speed ALWAYS check your units!. Linear speed v is linear speed units: length per time s is distance traveled in t

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Modeling with Sine Functions

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  1. Modeling with Sine Functions

  2. Circular Motion • Linear speed • Units are always length per time • mph (bike or car speeds) • Angular speed • rpm (revolutions per minute) • Engine speed • ALWAYS check your units!

  3. Linear speed • v is linear speed units: length per time • s is distance traveled in t • t is time it took to go s distance • Angular speed • the central angle (in radians) • the angular speed is revolutions per minute

  4. Examples • A 15-inch diameter tire on a car makes 9.3 revolutions per second. • Find the angular speed of the tire in radians per second. • Find the linear speed of the car. • A satellite in a circular orbit 1250 kilo-meters above Earth makes one complete revolution every 110 minutes. What is its linear speed? Assume that Earth is a sphere of radius 6400 kilometers

  5. Solutions • Change 9.3 revolutions per second to radians per second = 18.6π radians per second • Angular speed = (18.6π)/ 1 = 18.6π radians per second • Linear speed = rω = (7.5)(18.6π) = 438.252 inches per second • Linear speed

  6. Modeling Data in the Calculator • If there is a list of data points we can use the calculator to help find the line of best fit • Steps: • Put the data into L1 and L2 • Turn STAT plot on • Use zoom stat • Use sinreg to find sine function of best fit

  7. Monthly Temperatures for Chicago • Using your calculator, draw a scatter plot of the data for one period • Using your calculator find a sine function that best fits the data • Draw this function on the same graph as your scatter plot

  8. Monthly Temperatures for Chicago

  9. Homework! p. 699 # 21, 22 And yes… I will be checking it 

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