Asked by Ciara

The temperature in Fairbanks is approximated by
T(x)=37sin{2π/365(x−101)}+25
where​ T(x) is the temperature on day​ x, with x=1 corresponding to Jan. 1 and x=365 corresponding to Dec. 31. Estimate the temperature on day 342.
Answered by Steve
well, geez -- just plug in 342 for x, and use your calculator, or any of a multitude of online calculators.
Answered by Reiny
just plug in 342 for the x, and grind it out.
let me know what you get.

Here is a graph to help you check your answer.
http://www.wolframalpha.com/input/?i=plot+y+%3D+37sin%7B2%CF%80%2F365(x%E2%88%92101)%7D%2B25
Answered by Reiny
btw, make sure your calculator is set to radians, and not degrees
Answered by Steve
Hmmm. I don't know -- it's a question about temperature, so maybe degrees is better!

My question is, how do I set my calculator to Fahrenheit vs Celsius degrees?
Answered by Ciara
Came up with -11.48. But thats not correct answer
Answered by Reiny
Woahh there.
looking at the function, it will have a maximum of 37+25 or 62 and a minimum of -37+25 or -12
Since this is apparently Alaska, those units can only be in Fahrenheit units and not Celsius.

The units I was talking about are "radians" vs "angles measured in degrees" . The presence of π in sin(2π/365(x-101)) strongly suggests we have to have our calculator in radians.
On your calculator look for a key labeled DRG, it will cycle through degrees(D), radians(R) and gradients(G).
You want your calculator to show something like RAD , then use your trig buttons
I get
T(x)=37sin{2π/365(x−101)}+25
T(342)=37sin{2π/365(342−101)}+25
T(342)=37sin{2π/365(241)}+25
T(342)=37sin{4.1486...}+25
= 37(-.845249...) + 25
= appr -6.27

which might be quite balmy for Dec 8 in Alaska
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