Trigometric equations

[mclol]

Ok a guy is walking around a route from 6am to 945am during they made 3 complete rounds of a walk. she reaches a checkpoint 15 minutes after there house the greatest different they are away from the checkpoint is 15 minutes

A)write a circular function that describes the distance away from the checkpoint
I think I got this with my equation being y=1.5 sin 3(x+2pi)
but I can not for the life of me work out B
B) at exactly 7:38am how far way from the checkpoint are they.
Any help would be awesome Tia.

 

[HallsofIvy]

Ok a guy is walking around a route from 6am to 945am during they made 3 complete rounds of a walk. she reaches a checkpoint 15 minutes after there house the greatest different they are away from the checkpoint is 15 minutes

"A guy", "they", "she"??

A)write a circular function that describes the distance away from the checkpoint

I don't see how you can do this having some statement of distance such as the radius of the route. But all you give is time.

I think I got this with my equation being y=1.5 sin 3(x+2pi)
but I can not for the life of me work out B
B) at exactly 7:38am how far way from the checkpoint are they.
Any help would be awesome Tia.

I recommend you go back and read the problem again. Either you have quoted it incorrectly or you have left something out. Perhaps that "the greatest different they are away from the checkpoint is 15 minutes" should have been "the greatest distance they are away from the check point is 15 miles"?

 

[mclol]

Sorry I should not paraphrase

The question is a guard walks around in a circular function. starts walk at 6am finsihes at 9:45am during that time she has made 3 complete tours. the guard starts at the guardhouse and 15 mins later arrives at the checkpoint. greatest distance away form the checkpoint is 1.5k
A) write a circular function which ive done
I got y=1.5 sin3 (x+2pi)
B) At exactly 7:38am how far away from the check point is the guard
any help would be really god I'm really stumped.

 

[Ishuda]

Ok a guy is walking around a route from 6am to 945am during they made 3 complete rounds of a walk. she reaches a checkpoint 15 minutes after there house the greatest different they are away from the checkpoint is 15 minutes

A)write a circular function that describes the distance away from the checkpoint
I think I got this with my equation being y=1.5 sin 3(x+2pi)
but I can not for the life of me work out B
B) at exactly 7:38am how far way from the checkpoint are they.
Any help would be awesome Tia.

OK, let's start at the beginning. What is an appropriate definition of a circle in this situation. You have part of the answer but got it slightly wrong (y should be a function of time, not of x), so
x = a cos(b (t + c))
y = a sin(b (t + c))
Let's measure time from 6am, i.e. t = actual time - 6.00

In three hrs and 45 min (t = 3.75) they make 3 three complete rounds so in 1.25 hrs they make 1 complete round so the period is 1.25 hrs. That means the argument of the trig functions go through a complete cycle in 1.25 hrs, so what is b?

You should try to answer the questions yourself but if you are stuck, highlight the section between the >>> and <<< for a hint/answer.
>>>
sin(b (t + c)) = sin(b (t + 1.25 + c)) = sin(b (t + c) + 2 \(\displaystyle \pi\))
b = 1.6 \(\displaystyle \pi\)
<<<

Call the line formed by the center location at (x,y) = (0,0) and where they are at time t=.25 (at the checkpoint), the y axis, i.e. y=0 at t=0.25. So, c is what?
>>>
-0.25
<<<

The maximum distance you can get from a fixed point on a circle if you have to stay on the circle is straight across the circle, i.e. the diameter of the circle. Well we know the radius of the circle is a (x² + y² = a²) and the radius is half the diameter so a is what?
>>>
7.5
<<<
and the final equations are what? Also don't forget that time is in hours measured from 6am.
>>>
x = 7.5 cos( 1.6 \(\displaystyle \pi\) (t - 0.25) )
y = 7.5 sin( 1.6 \(\displaystyle \pi\) (t - 0.25) )
<<<

 

[mclol]

OK, let's start at the beginning. What is an appropriate definition of a circle in this situation. You have part of the answer but got it slightly wrong (y should be a function of time, not of x), so
x = a cos(b (t + c))
y = a sin(b (t + c))
Let's measure time from 6am, i.e. t = actual time - 6.00

In three hrs and 45 min (t = 3.75) they make 3 three complete rounds so in 1.25 hrs they make 1 complete round so the period is 1.25 hrs. That means the argument of the trig functions go through a complete cycle in 1.25 hrs, so what is b?

You should try to answer the questions yourself but if you are stuck, highlight the section between the >>> and <<< for a hint/answer.
>>>
sin(b (t + c)) = sin(b (t + 1.25 + c)) = sin(b (t + c) + 2 \(\displaystyle \pi\))
b = 1.6 \(\displaystyle \pi\)
<<<

Call the line formed by the center location at (x,y) = (0,0) and where they are at time t=.25 (at the checkpoint), the y axis, i.e. y=0 at t=0.25. So, c is what?
>>>
-0.25
<<<

The maximum distance you can get from a fixed point on a circle if you have to stay on the circle is straight across the circle, i.e. the diameter of the circle. Well we know the radius of the circle is a (x² + y² = a²) and the radius is half the diameter so a is what?
>>>
7.5
<<<
and the final equations are what? Also don't forget that time is in hours measured from 6am.
>>>
x = 7.5 cos( 1.6 \(\displaystyle \pi\) (t - 0.25) )
y = 7.5 sin( 1.6 \(\displaystyle \pi\) (t - 0.25) )
<<<

Hi thank you for the help but the answer should in a sin wave function for a

 

[stapel]

Hi thank you for the help but the answer should in a sin wave function for a

So, based on the extensive helps, hints, and suggestions you've been provided, what have you done?

Please reply showing all of your work and reasoning. Thank you.

 

[mclol]

So, based on the extensive helps, hints, and suggestions you've been provided, what have you done?

Please reply showing all of your work and reasoning. Thank you.

Ok i got the sin wave function because
general exaustion y=AsinN(x-b)+c
A=Amplitude = 1.5 because that is the greatest distances away from the checkpoint.
N=3 because that is the number of cycles
b=2pi because that is the raidences of a circle
c=0 because there is no phase shift.
therefor my equation was y=1.5sin3 (x +2pi)
I had to plot it which is the pic

So all I need to work out is at 7:38 am how far is she away from the checkpoint
I got told to convert time to raidians but not to sure on how to go about it.