Part 1: Do Adam and Beth travel the same distance during the ride? Choose a distance that each seat (horse and dragon) sits from the center and use the radius to determine how far each would travel during one rotation.

Adam's distance from the center: 14 ft

Circumference = (2pi)*r = (2pi)*14 = 87.92ft

Beth's distance from the center: 7 ft

Circumference: =(2pi)*r = (2pi)*7 = 43.96ft

Adam and Beth do not travel the same distance on the ride. Adam travels a farther distance because his seat farther from the center of the ride.

**10.03 Module 10 Quiz**

Part 2: Choose an angle of rotation. Using complete sentences, compare the distance Adam and Beth will travel during this angle measurement.

The distance from Robbie to the Earth's center is 10,000 km (3600+6400). The angle is 350.

x:10,000(cos350) = 9848

y: 10,000(sin350) = 1736

So the coordinate is (9848, 1736)

Robbie the Robot is on a weather satellite orbiting

Earth about 3600 km above the surface. The Earth’s radius

is about 6400 km. He has had a malfunction in his output device, and the satellite is traveling without communication. His last report was only in terms of trigonometric values and was only partially received. It said, sin Θ < 0….. and then he was lost again.

Part 1: Create a set of coordinates that would be reasonable for Robbie’s position in space and satisfy his last, partial report. Using complete sentences, describe Robbie’s location and your reasoning.

Angle of rotation: 90 degrees (pi/2)

Adam: (pi/2)*14= 21.98 feet So Adam travels about 66 feet less in this angle of rotation than he does in a full rotation

Beth: (pi/2)*7= 10.99 So Beth travels about 33 feet less in this angle of rotation than she does in a full rotation

Part 3: Using complete sentences, describe which position you would prefer and why.

I would prefer Adam's seat on the outermost part of the carousel because he went the farthest. Although they were on the same ride at the same time, Adam got more out of the ride because beth didnt ride as far technically.

Part 2: What are the values of the sin Θ, cos Θ, and tan Θ using your coordinate point?

sin=1736/10000= 0.1736

cos=9848/10000= 0.9848

tan=1736/9848= 0.1763

When would degree measure be appropriate?

When would radians be a better choice?

What are the pros and cons of each?

Both degrees and radians measure angle rotations. However, land and sea navigators use degrees while engineers and software developers use radians. Radians would be a better choice to calculate distance while building bridges. Degrees are more often used in everyday work situations.