# 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.