Mathematics
darkknight:

precalc

darkknight:

darkknight:

@justjm

darkknight:

darkknight:

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

darkknight:

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

hep:

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

justjm:

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 $$(x,y)=(rsinθ, rcosθ)$$

darkknight:

so just radius times sin and cos of 34?

justjm:

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

darkknight:

btw its (rcosθ,rsinθ)

darkknight:

thx

darkknight:

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

justjm:

$$\color{#0cbb34}{\text{Originally Posted by}}$$ @darkknight btw its (rcosθ,rsinθ) $$\color{#0cbb34}{\text{End of Quote}}$$ OH shoot you're right sorry my bad. xD

justjm:

let me take a look..

justjm:

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] $$\theta = \omega t+\theta_o$$ $$\omega = 3\ \frac{rev}{\min}$$, $$t=6 s$$ $$∴ \theta =\left(3\ \frac{rev}{\min}\cdot\frac{1\ \min}{60\ \sec}\right)6\ \sec\ =\ 0.3 ~rev$$ $$0.3\ rev\ \cdot\frac{360°}{1\ rev}=108°$$ $$108°+(-14°)=94°$$

justjm:

Similarly in (d) you'll need to use the same equation(s) $$\theta=\omega t$$ $$\theta_f = \omega t + \theta_i$$

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?

justjm:

$$\color{#0cbb34}{\text{Originally Posted by}}$$ @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

darkknight:

wow! Thank you

justjm:

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