-14.4 December -5.3 November 5.3 October 12.3 September 18.5 August 19.5 July 17.0 June 12.0 May 4.0 April -6.1 March -13.6 February -17.8 January Average temperature (C) Month
a.) Sketch the graph of the sinusoidal function given at the second slide. If you get something like this you got it right!!! In order to get this graph we look at the maximum and minimum values and when they occur. The minimum value is -17.8 and it happen during January. The minimum value is at (1, -17.8). How did I get 1? I got one because January is the first month of the year. The maximum value is 19.5 and it happen during July, the seventh month of the year so the maximum value is at (7, 19.5) Remember to put arrows on both of your axis and label it if needed!!!
b.) Write two equations for the function; one using sine and other using cosine. First of all I’m going to tell you about the two basic trigonometric functions: They are just the same the only difference is the phase shift of
Parameter A It is called the amplitude. It is the distance of the maximum and minimum values from the sinusoidal axis. It is always positive, there is no such thing as a negative distance. We can get the amplitude by using this formula:
Parameter B Parameter B is not the period it determines the period according to this relation: OR Period is the distance along the x-axis required to make one wave. Why 12 ? Because there are 12 months in one year.
Parameter C It is the phase shift or the horizontal shift. WATCH OUT FOR ITS SIGN.. COSINE A general cosine function starts at the maximum. But on this case the maximum is shifted 7 units to the right so C=7 SINE A general sine function starts at the average value on this case the average value was shifted 4 units to the right so C=4.
Parameter D It is the vertical shift or average value. It determines the sinusoidal axis. You can get it by using the formula below: OR So Parameter D=0.85
Now that we have all the parameters we can now get the two equations.