Modeling with Sine Functions

Circular MotionLinear speed

Units are always length per time mph (bike or car speeds)

Angular speedrpm (revolutions per minute)

Engine speed

ALWAYS check your units!

Linear speed

v is linear speed units: length per times is distance traveled in tt is time it took to go s distance

Angular speed

t

sv

t

rv

• the central angle (in radians)• the angular speed is

revolutions per minute

Examples1. A 15-inch diameter tire on a car makes 9.3

revolutions per second.a) Find the angular speed of the tire in radians

per second.b) Find the linear speed of the car.

2. 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

Solutions1. Change 9.3 revolutions per second to

radians per second = 18.6π radians per second

a) Angular speed = (18.6π)/ 1 = 18.6π radians per second

b) Linear speed = rω = (7.5)(18.6π) = 438.252 inches per second

2. Linear speed rad/min 220rev 1

rad 2

min

rev 110

km 7650km 1250km 6400 r

km/min 52873002207650 r

Modeling Data in the CalculatorIf there is a list of data points we can use the

calculator to help find the line of best fitSteps:

Put the data into L1 and L2Turn STAT plot on

Use zoom statUse sinreg to find sine function of best fit

Monthly Temperatures for Chicago

a) Using your calculator, draw a scatter plot of the data for one period

b) Using your calculator find a sine function that best fits the data

c) Draw this function on the same graph as your scatter plot

Month, x Average Monthly Temp,

degrees F

January 25

February 28

March 36

April 48

May 61

June 72

July 74

August 75

September 66

October 55

November 39

December 28

Monthly Temperatures for Chicago

459.50)175.25209sin(.82.25 xy

Homework!p. 699 # 21, 22

And yes… I will be checking it