I have a question I do not think anybody answered it

Question

Researches find a creature form an alienplanet. Its body temperature is varying sinusoidally with time. 35 min after they start timing, it reaches a high of 120 F. 20 min after that it reaches its next low, 104 F.

How do I come up with this equation I'm getting this

y = 8 sin (pi X)/20

I do not know if there is a phase sift in this equation I'm obviously doing something worng please tell me how to come up with this equation thank you

Answer 1

you are right on the amplitude 8.

Now half of period is 20 min. So period is 40 min, it needs a 35/40 *PI shift.

check that.

Answer 2

how do we now that the phase shift is (35pi)/40

please explain

THANKS

Answer 3

Lets do it again:

the average temp is 112

temp=112+8sin(wt+theta)

now, you know a zero is between 10 min before the high. Which is 25 min after start.
Theta= 25*2PI/40=3.93 radians

temp= 112+ 8 sin(wt-3.93)
and w= 2PI/40
check
temp at 35:
temp=112+8sin(2PI/40 *35-3.93)=120

I hope that helps.