**MADE TYPO ON SLIDE WITH GRAPH, FULL PERIOD IS 362 NOT 352
a) Graph
Find day of max and min: -max is where x=0 because that is our starting point for this graph January 1 -to find day of min add up number of days from jan to june -we're making february only 28 days -after adding it all up our min should be on the 181th day!
Drawing graph: -x axis is days, y is temperature -when x=0 is January 1 -we're given the max and min -knowing max and min we know half a period, multiply by 2 to get full period of 362 -make your 4 ticks quickly for the days -full period is 362, 3/4 of a period is 271.5, 1/2 a period is 181, 1/4 a period is 90.5 -max temp of 37 and min temp of 15, we need to find the avg value -write down the max and min values on the y axis -avg value = (37+15)/2, which is 26! -so you should have a point on (0,37) which is the max and a point on (181, 15) the min -this is a cosine graph since it starts at its max point -pattern of a cosine graph is it will go to its max point then to its avg value then to its min back up to its avg value and up to its max
b)Equation:
A=amplitude can be found by finding the difference of the max and avg value or the difference of the average value and the min B=2pi/period C=phase shift is the number of units the graph moved from the original sine or cosine graphs on the x axis D=avg value
Cosine A= 11 B=2pi/362 c= no phase shift since it already starts at its max point D=26
Sine **sine and cosine are related by pi/2 units on the x axis**
A=-11 (negative sign flips the graph over so it goes from its min to avg value to max) B=2pi/362 C=-90.5 (sine graph starts on its avg value, 90.5 is the value of which the cosine graph is at its avg value so we must minus 90.5 to move the graph left) D=26
c)Finding the temperature on March 17
-first find the how many days from January to march 17 there is -that is 76 days -then all that is left to do is to plug it in plug it in -plugging the value into the cosine would be a faster way to get the answer since it has no phase shift