Results 1 to 3 of 3

Math Help - Help with general trig equation

  1. #1
    Newbie
    Joined
    Mar 2010
    Posts
    3

    Help with general trig equation

    I don't know what this problem would be classified as, but i need help with it!

    The formula F(x)=75+15sin[2π/365(x-101)] represents the fahrenheit temperature in Gainesville as a function of the day of the year. Let x represent the day of the year (in a non leap year), so x=1 represents Jan. 1 (etc.) Use this formula to determine the day(s) of the year (give the dates) when the average daily temperature will be closest to 85F

    I graphed it in a graphing calculator and determined that the days were day 143 and day 240 (April 23rd and July 28) and plugged them into the equation and they equaled about 85, but i do not know how to work the problem out using trig functions.

    Any help would be appreciated. Thank you!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    -1
    e^(i*pi)'s Avatar
    Joined
    Feb 2009
    From
    West Midlands, England
    Posts
    3,053
    Thanks
    1
    Quote Originally Posted by baconfoot View Post
    I don't know what this problem would be classified as, but i need help with it!

    The formula F(x)=75+15sin[2π/365(x-101)] represents the fahrenheit temperature in Gainesville as a function of the day of the year. Let x represent the day of the year (in a non leap year), so x=1 represents Jan. 1 (etc.) Use this formula to determine the day(s) of the year (give the dates) when the average daily temperature will be closest to 85F

    I graphed it in a graphing calculator and determined that the days were day 143 and day 240 (April 23rd and July 28) and plugged them into the equation and they equaled about 85, but i do not know how to work the problem out using trig functions.

    Any help would be appreciated. Thank you!
    Work backwards and use arcsin (inverse sine)

    \frac{F(x) - 75}{15} = \sin \left(\frac{2\pi}{365}(x-101)\right)

    \arcsin \left(\frac{F(x) - 75}{15}\right) = \left(\frac{2\pi}{365}(x-101)\right)


    x-101 = \frac{365}{2\pi} \times \arcsin \left(\frac{F(x) - 75}{15}\right)

    x = 101 + \frac{365}{2\pi} \times \arcsin \left(\frac{F(x) - 75}{15}\right)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Mar 2010
    Posts
    3
    hey thanks so much!
    but how do I get to 240? I tried to use the reference angle, but apparently thats not right.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. general solution of trig equation
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: September 14th 2011, 07:40 AM
  2. Trig General Solutions
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: June 5th 2009, 05:08 PM
  3. general solution ,trig?
    Posted in the Calculus Forum
    Replies: 7
    Last Post: June 1st 2009, 06:57 PM
  4. general solution to trig problem
    Posted in the Trigonometry Forum
    Replies: 10
    Last Post: May 18th 2009, 02:28 PM
  5. Replies: 2
    Last Post: May 18th 2009, 12:51 PM

Search Tags


/mathhelpforum @mathhelpforum