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.
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
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
btw, make sure your calculator is set to radians, and not degrees
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?
Came up with -11.48. But thats not correct answer
To estimate the temperature on day 342, we can substitute the value of 342 into the equation T(x). Let's go step by step:
Step 1: Start with the given equation:
T(x) = 37sin(2π/365(x−101)) + 25
Step 2: Substitute x = 342 into the equation:
T(342) = 37sin(2π/365(342−101)) + 25
Step 3: Simplify the expression inside the sine function:
T(342) = 37sin(2π/365(241)) + 25
Step 4: Calculate the value inside the sine function:
T(342) = 37sin(2π/365(241))
Step 5: Use a calculator to evaluate the sine function:
T(342) ≈ 37sin(1.673)
Step 6: Calculate the sine of 1.673 using a calculator:
T(342) ≈ 37(0.991)
Step 7: Simplify the expression:
T(342) ≈ 36.767
So, the estimated temperature on day 342 is approximately 36.767 degrees Fahrenheit in Fairbanks.