Trigonometry Question

Question

The temperature of a particular patient in a hospital ranges between 94ºF and 100ºF as modeled by the following function where t is the time in hours:

T(t)=3sin((π*t)/14) +C 

What is the value of C for this function?

A. 97ºF

B. 96ºF

C. 95ºF 

D. 94ºF

Answer 1

T(t)=3sin((π*t)/14) +C

Now we see in steps how you can solve this easily

We all know that the value of sin ranges from -1 to 1

now in the first case sin(x)= -1 T(t)= 3*-1+97=94 as the case states

Next sin(x)= 1 so T(t) = 3*1 +97= 100

so we get range of temperatures that are supposed to be 94 and 100

avg =(94+100)/2=97

so the answer is 97 as only if the value is 97 the value of sin can properly oscillate between its values

of -1 to 1 .

Answer 2

A 97 degrees F

(100+94)/2 = 97

when sine of the angle = zero, the temperature is at the midpoint, or the average temperature = 97

T = 3(0) + 97

T =3(1) +97 =100 when sine of the angle = 1

when sine of the angle =-1, T =3(-1) +97 = 94

Answer 3

Hello, Kevin,

y=3*sin((3.17*x)/14))+C

The equation is that of a sine wave that is offset from 0 by C. I will assume the since wave portion predicts the fluctuation from C as a function of time. We are told that the temperatures ranges from 94F to 100F, so the sine wave should reflect this range of values as a function of time. I'm not sure how to solve this other than to graph the function y=3*sin((3.17*x)/14)) and then find the value of C that would move the graph to a point whater a maximum is at 100F and a minimum of 94F.

I did that in Desmos and set the C as a variable adjustable with a slider. By moving the slder to C = 97, the sine wave meets the above criteria.

Here is the plot: https://www.desmos.com/calculator/g9q1rbyyfd