Question

TRIG HELP PLEASE!!!!!!!!!

I just need help w part 2!!

Adam and Beth decide to ride the carousel. Adam picked a horse on the outside edge and Beth chose a dragon on the inside, closer to the center.
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.

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

Answer 1

I chose 12 as the distance for adam and 4 as the distance for beth

Answer 2

So, it should be \[s=r \theta \] for your formula. s is the arc length and r is the radius (12 for adam, 4 for beth). Just choose the angle and plug it into the formula.

Answer 3

@wrstlr3232 idg how i choose an angle? like just choose any random angle?

Answer 4

Yeah, from the question in part 2, it says choose an angle of rotation. You should be able to choose any angle as long as it's the same for each person. It would be easier to do if you are in radians for the angle.
I guess I didn't actually answer your question about using the complete sentence. I would put something like, since adam is further from the center, he must travel further to reach the same angle as beth. then maybe include the formula and how you solve it.

Answer 5

@wrstlr3232 Sooo i can choose say 150 degrees? and convert that to radians?

Answer 6

Yep. The question is more or less asking what happens when you get further away from the center. Then using the angle of rotation as proof. Do you know how to convert to radians? It took me forever to learn how to convert haha.

Answer 7

@wrstlr3232 yeah!! it would be 5pi/6 right? now do i multiply that with the radii?

Answer 8

Perfect. If you take 5pi/6 you get 2.61799. So you'd have \[s=12(2.61799)~~~~~~s=4(2.61799)\]
That will give you the arc length for Adam and the arc length for Beth, respectively. If you find s for each of them, Adam travels 31.41units and Beth travels 10.47units

Answer 9

Or you could just multiply 5pi/6 by 12 and 4 and you'd have 60pi/6 and 20pi/6

Answer 10

I thought I'd multiply them by the radius so 6 and 2 not 12 and 4?

Answer 11

since its r(theta)

Answer 12

Oh ok, yeah that's right. Sorry I thought you wanted the radius to be 12 and 4.

Answer 13

Just checking :) so when i do that its 5pi and 5pi/3.. so those are the distances they travel?

Answer 14

Correct. It's easier to think if you multiply it out. So like 5*pi=15.7. So say Adam was 6...meters from the center and he goes around 150degrees. He traveled 15.7 meters. I would keep it as 5pi because it looks cleaner. But sometimes it's easier to see if you actually do the calculations.

Answer 15

Thank you so so so much!! I really appreciate your help thank you :) um how do you give a medal to someone? lol

Answer 16

Haha, no problem. I'm glad you asked questions and not just looked for the answer.