Question

Trig~ why? :(
Two gears are connected and are rotating simultaneously. The smaller gear has a radius of 4 inches and the larger gear has a radius of 7 inches

Answer 1

u do realize this is a test question

Answer 2

sorry, was on my phone

Answer 3

if they are rotating simultaneously, it is because their teeth are engaging with each other mechanically...

Answer 4

Part 1: What is the angle measure, in degrees and rounded to the nearest tenth, through which the larger gear has rotated when the smaller gear has made one complete rotation?

Part 2: How many rotations will the smaller gear make during one complete rotation of the larger gear?

Answer 5

the direction of the other is opposite to the other...

Answer 6

@Orion1213 what are you talking about?

Answer 7

cause you did not post the real question, it's only now you post it?

Answer 8

Yes I posted the real question and the part 1 and part 2

Answer 9

trig isn't my cup of tea

Answer 10

@Orion1213 are you able to help me a bit?

Answer 11

i'm reviewing the concept applicable... or maybe the others viewing this have already the idea...

Answer 12

Would in part 1 be 360/7?

Answer 13

for part 1... if we consider the length of the arc traveled by small gear... it would be \(S=\theta r\) where \(\theta\) must be in radians... actually a complete revolution for small gear is just computing its circumference \(C=2 \pi(4)=8 \pi\) inches...

If this will be the same arc length we consider for larger gear, we will get the equivalent angle it would make, such as \[8\pi=\theta_B (7)\]\[\theta_B=\frac{8\pi}{7}\times \frac{180°}{\pi}=205.71428571428571°\approx 205.7°\]

Answer 14

im sorry, I kind of figured it out already. I went back to my notes and I got that same answer but thanks at least I feel good you got the same answer

Answer 15

here's a metal for helping.

Answer 16

so it's a matter of ratio between arc length as well as circumference...

Answer 17

thanks... no problem... :-)