Question

precalc

Answer 1

This is my work.

Answer 2

So my precalc teacher told me that the formula for sinusoidal parametrics are
\[a(\sin((2\pi/b(t-Cx))+d, a(\sin((2\pi/b(t-Cy))+d\]
Where a is radius
b is the amount of time it takes for 1 rotation
d = how far center is from x-axis
Cx = (-initial position +pi/2) (1/(2pi/b))
Cy = (-initial position) (1/(2pi/b))

Answer 3

@dude, @hero, @Hero @Vocaloid?

Answer 4

Got no clue where i messed up

Answer 5

@InsatiableSuffering

Answer 6

@hartnn @imqwerty 💀

Answer 7

wait I think i may have gotten it

Answer 8

nah, can't catch it yet. Ill redo the problem and tell u guys if i find anything

Answer 9

Hold on, I got a different answer. Will show once I confirm it

Answer 10

uhh, now I got this for my coordinates:
−26.21629336, −24.79534305

Answer 11

New show my work:

Answer 12

this is wrong too. Because according to the coordinates. the distance from the origin should be 29, not the 36 i am getting

Answer 13

Did you take the origin as the center of the merry go round?

Answer 14

Yes,

Answer 15

Ya think we have to do otherwise @imqwerty ?

Answer 16

Nope, since they haven't specified any origin, it's alright to consider the center of the wheel as the origin.

Answer 17

How did you calculate the initial position?

Answer 18

Initial position is 20 degrees. So 20(pi/180) is pi/9 radians

Answer 19

Alright, and you've considered d as 0, correct?

Answer 20

yes i have. And I think I know why I messed up last time too

Answer 21

Yeah found my original mistake. So Instead of reading 1/(2pi/(1/6)) i read it as 1/2pi)/(1/6)

Answer 22

Don't have the answer yet thou

Answer 23

workin on it

Answer 24

aight

Answer 25

hmm interesting. I got the answer I got the very first time

Answer 26

-21.58994668, −21.0510889)? but I know that can't be right either.
I am messing up somewhere

Answer 27

I think that is not correct

Answer 28

yes it isn't. Because the distance from that to the origin isn't the radius (29)

Answer 29

yup, are you sure that the equation that you're using is correct?

Answer 30

Yes, confirmed

Answer 31

the wheel rotates 6 times in a minute.
the given time is 6mins so the wheel will make 6*6 = 36 complete rotations. Which means that you'll return to your initial position after 6 minutes

Answer 32

So now we have to find the position at 20 degrees.
So do we do something like tan(20) = oppo/adj?

Answer 33

\(\color{#0cbb34}{\text{Originally Posted by}}\) @darkknight
So my precalc teacher told me that the formula for sinusoidal parametrics are
\[a(\sin((2\pi/b(t-Cx))+d, a(\sin((2\pi/b(t-Cy))+d\]
Where a is radius
b is the amount of time it takes for 1 rotation
d = how far center is from x-axis
Cx = (-initial position +pi/2) (1/(2pi/b))
Cy = (-initial position) (1/(2pi/b))
\(\color{#0cbb34}{\text{End of Quote}}\)
are you sure they're both sin? i think one of them should be a cos

Answer 34

apparently sinusoidal functions, are supposed to be sin. Not cos. The formula is correct for a sinusoidal equation but I don't think that is what we have to do here

Answer 35

cos works as well because you can covert between sin and cos

Answer 36

I just checked it and the equations are correct. They simplify to this-

\(acos(2\pi \omega t + \theta) + d,~ asin(2 \pi \omega t + \theta) + d \)

you're probably making some calculation mistake

Answer 37

\(\Large\frac{1}{\frac{2\pi}{\frac{1}{6}}} = \frac{1}{12\pi}\)

Answer 38

yes I just got that. And It let to my first answer which is wrong. If you are so sure let me retry the problem

Answer 39

"acos(2πωt+θ)+d" Are you sure. My teacher said a(sin(...

Answer 40

this is confusing

Answer 41

Okay! I am actually big dumb. Thanks @imqwerty and all that has helped. We don't talk about not putting the calculator in radian mode.

Answer 42

oh nice one. in alg 2 we do degrees

Answer 43

you know, I was doing the entire problem again and was gonna ask my teacher. But based off what imqwerty said it has to be in the first quadrant. So i was wondering why I was wrong. Figured out why at least xD

Answer 44

Let this be a lesson to all.
REMEMBER WHAT MODE YOUR CALCULATOR IS IN!!!

Answer 45

\(\color{#0cbb34}{\text{Originally Posted by}}\) @darkknight
"acos(2πωt+θ)+d" Are you sure. My teacher said a(sin(...
\(\color{#0cbb34}{\text{End of Quote}}\)
yeah, it's the same thing, but simplified

Answer 46

Oh okay.