Warm Up:

r = 237

A

B

1. Find the length of arc AB in each problem:

A

B

122

r = 9

2. Write the equation of the circle in standard form:

x2

+ 6x

+ 12

+ y2

= 12

Then identify the center and the radius:

Homework Questions:

Yesterdays Notes:

Daytona International Speedway is 2.5 miles long.

The diameter of the racecar tire is 25 inches.

It can make approximately 60500 revolutions before needing to be replaced.

Approximately how many laps can the tire make around the speedway before needing to be replaced?

Hint:

Once you find the total distance the wheels can travel, you will have to convert inches to feet and then to miles. (1 mile = 5280 feet).

Daytona Exploration:

Notes:

Radians: a standard unit of angular measure

r = 1

In a unit circle there are _________ radians

around the entire thing, instead of ________ degrees.

The measures, in radians of:

180:

90:

270:

3 1 1

x

A

B

A'

A''

B'

Find the arc lengths of AB, A'B' and A"B". Leave it in terms of pi.

length of arc AB:

length of arc A'B':

length of arc A"B":

Radian measure of an arc : arc length/radius

Therefore: Arc length =

3 1 1

x

A

B

A'

A''

B'

Find the radian measure of each arc:

AB:

A'B'

A"B"

Notice something?

Then use radian measure x radius to find arc length again. Leave it in terms of pi.

Notice something?

Therefore:

The length of an arc can be found two ways:

Using a proportion, and....

Arc XY has a degree measure of 60.Find the radian measure of 60 degrees by finding the arc length of XY in a circle of radius 3.

Find the length of arc XY in circles of radii 4 and 5. Using the radian measure:

3 45

X

Y

X

Y

X

Y

Attachments

11.4 day one.notebook