Question

quick question see attached

Answer 1

\[h=139-125\cos\frac{ \pi }{ 10 }t\]
where h is given in feet and t is given in minutes - use this equation to find the times at which the passengers will be 100 ft above the ground
got to this point and stuck
\[\cos \frac{ \pi }{ 10}t=0.312\]

Answer 2

@jdoe0001 @whpalmer4 @robtobey

Answer 3

h=139+Cos[\[Pi] 10 t] ?

Answer 4

i have solutions book and its saying
\[\frac{ \pi }{ 10 }t=1.233+2\pi k \]
or \[\frac{ \pi }{ 10}t=(2\pi-1.253)+2\pi k\]
where does this come from ?

Answer 5

i set original equation to
\[100=139-125\cos \frac{ \pi }{ 10 }t\]
then got to \[\cos \frac{ \pi }{ 10 }t=0.312\]
now what ?

Answer 6

@e.mccormick

Answer 7

t is not yet alone.

Answer 8

And is it \(\cos \frac{ \pi }{ 10 }t\) or \(\cos \left(\frac{ \pi }{ 10 }t\right)\)?

Answer 9

first one

Answer 10

OK. Then what is \(\dfrac{0.312}{\cos \frac{ \pi }{ 10 }}\) ?

Answer 11

is it:\[\cos(\frac{ \pi }{ 10 }t)\]
or:\[\cos(\frac{ \pi }{ 10 })t\]

Answer 12

I already asked that.

Answer 13

but did he understand it as that

Answer 14

or she

Answer 15

i just dont understand how they got to \[\frac{ \pi }{ 10}t=1.253+2\pi k\]
or \[\frac{ \pi }{ 10}t=(2\pi-1.253)+2\pi k \]
is in solutions book how do u get to that point its as i have it written in original no ( )

Answer 16

2pik means it is + a multiple of 2pi

Answer 17

because cosine has a period of 2pi

Answer 18

Refer to the Mathematica attachment.

Answer 19

ok yes i know that but how do i get from \[\cos \frac{ \pi }{ 10 }t=0.312 \]

Answer 20

answer is saying 4.0 minutes and 16.0 minutes i just want to know how to get that point in previous post :/

Answer 21

\(100=139-125\cos \frac{ \pi }{ 10 }t\)
\(-39=-125\cos \frac{ \pi }{ 10 }t\)


The reason we keep asking is simple. If it is:
\(\cos \left(\dfrac{ \pi }{ 10 }\right) t\)
Then it is a basic calculation and only at one point.

On the other hand, if it is:
\(\cos \left(\dfrac{ \pi }{ 10 }t \right) \) then it means:
\(\cos \left(\dfrac{ t\pi }{ 10 } \right) \)

And you have to isolate things a completely different way.

It just looks odd for them to have put the t at the end like that. And what Rob did, \(\cos \left(10\pi t \right) \) is also possible, and makes sense for changing how it was written into something that looks like it maight have been done in a book. Something is simply wrong in how it was written.

Answer 22

ok so even if that how do i get to the point where it is no cos just to the point in previous post

Answer 23

going to post the picture of what i have for solution manual

Answer 24

does this help? lol

Answer 25

It looks like they took the arccos of both sides.

Answer 26

ohhh ok that helps haha!! that was what i was confused at how they got lol!!

Answer 27

\(\arccos(.312) \approx 1.25349894 \) in radians

Answer 28

yes ok makes sense!!

Answer 29

And the rest is to deal with it being periodic.

Answer 30

With this being the cosine, it would be the x value that is critical.

Answer 31

thanks :D got it was just not sure how do get the other parts thanks !!

Answer 32

Kk. Have fun!