A group of scientists found a new species of spider in the desert. The body temperature of the spider appears to vary sinusoidal over time. A maximum body temperature of the spider reaches 125? after 15 minutes from the start of the examination. Then, 14 minutes later, the body temperature falls to a minimum of 99?. The scientists would like to write an equation to model the body temperature of the spider over time. Which function will model their findings?

Question

I got f(t)=13sin (pi/7(x-1)+122

Answer 1

amplitude is (125-99)/2 = 13
The center line is 125-13 = 112, not 122
2pi/k = 2*14, so k = pi/14
Since f(15) = 125, the max, that means that f(1) = 99, the minimum
cosx has a max at x=0, so -cos(x-1) has a minimum at x=1.

f(t) = 13 cos(pi/14 (x-1)) + 112

The graph at

http://www.wolframalpha.com/input/?i=-cos%28pi%2F14+%28x-1%29%29

shows that the cosine part has its first max at x=15 and its next min at x=29.

Answer 2

You left t out !

max at 15 min
min at 15+14 = 29
so
14 min from sin = +1 to sin = -1
that is half a period so T = 28 min

2pi t/T = 2 pi at t=T we disagree about all this so pi t/14 is 2 pi when t = T = 28

range from max to min = 2 A = 125-99 = 26
so
A = 13 (check with you :)

average = (125+99)/2 = 224/2 = 112 (check with you)
so so far

f(t) = 112 + 13 sin (pi t/14 - phase)
when t = 15, f(15) = 125

125 = 112 + 13 sin (pi*15/14 - phase)

sin (pi*15/14 - phase) = 1
so
(15/14) pi - phase = pi/2

phase = pi (8/14)
so
f(t) = 112 + 13 sin (pi t/14 - 8 pi/14)
or
f(t) = 112 + 13 sin [ (pi/14)(t-8) ]