Question

precalc

Answer 1

@justjm

Answer 2

I am soo stupid. Sorry I didn't post the problem and accidently posted the other thing twice

Answer 3

just need help on a) I don't know what to do so I guess once I know how to do a I can do the rest

Answer 4

Try 4 ×34 and then divide by 3 and see what it gets you

Answer 5

This question serves as an introduction to polar coordinates.

So for (a) the '4' minutes is just meant to trick you. Since it's going 3 RPM, after 4 minutes, it's done 12 revolutions but you're still at the same location where you were initially. Hence θ=34° and r=24. Now you can convert to rectangular coordinates using \((x,y)=(rsinθ, rcosθ)\)

Answer 6

so just radius times sin and cos of 34?

Answer 7

\(\color{#0cbb34}{\text{Originally Posted by}}\) @darkknight
so just radius times sin and cos of 34?
\(\color{#0cbb34}{\text{End of Quote}}\)
yes

Answer 8

btw its (rcosθ,rsinθ)

Answer 9

thx

Answer 10

What about for a problem like c where it doesn't end up in the same spot?

Answer 11

\(\color{#0cbb34}{\text{Originally Posted by}}\) @darkknight
btw its (rcosθ,rsinθ)
\(\color{#0cbb34}{\text{End of Quote}}\)
OH shoot

you're right sorry my bad.

xD

Answer 12

let me take a look..

Answer 13

I believe you need to use angular kinematics

\(\frac{d\theta}{dt}=\omega\)
\(d\theta=\omega dt \)
\( \int d\theta= \int \omega dt \)
\(\theta = \omega t+\theta_o\)
[you don't need to do the above, just know the formula]

\(\theta = \omega t+\theta_o\)

\(\omega = 3\ \frac{rev}{\min}\), \(t=6 s\)
\(∴ \theta =\left(3\ \frac{rev}{\min}\cdot\frac{1\ \min}{60\ \sec}\right)6\ \sec\ =\ 0.3 ~rev \)

\(0.3\ rev\ \cdot\frac{360°}{1\ rev}=108°\)

\(108°+(-14°)=94°\)

Answer 14

Similarly in (d) you'll need to use the same equation(s)

\(\theta=\omega t\)
\(\theta_f = \omega t + \theta_i\)

Answer 15

and once i get the angle (for example 94 degrees for c) I can just plug it into r cos theta and r sin theta and find the coordinates right?

Answer 16

\(\color{#0cbb34}{\text{Originally Posted by}}\) @darkknight
and once i get the angle (for example 94 degrees for c) I can just plug it into r cos theta and r sin theta and find the coordinates right?
\(\color{#0cbb34}{\text{End of Quote}}\)
yeah and r is the same ofc

Answer 17

wow! Thank you

Answer 18

\(\color{#0cbb34}{\text{Originally Posted by}}\) @darkknight
wow! Thank you
\(\color{#0cbb34}{\text{End of Quote}}\)
np