+118728 
+118728 Hi NinjaDragons98,
Here are the graphs. I have also included a colour coded line at the centre of the temperature limits.
Red Los Angeles
Green Osaka
Blue Buenos Aires
https://www.desmos.com/calculator/d2xfeenjdv
23) Osaka (B green) has the biggest temperature variation becasue at 20.71 degrees it has the biggest amplitude.
24) You can see from the graph that Osaka has the coldest temperatures so it is most likely to snow in winter.
ALSO
The lowest sin(anything) is is -1
so the lowest temperatures are
Los Angeles = -8.086+76.08 = 68 degrees
Osaka = -20.71+68.97 = 48 degrees
Buenos Aires = -13.03+72.38 = 59 degrees
so you can see from the algebra that Osaka gets the coldest.
25) Explain why the function for Buenos Aires has a positive horizonatal shift as opposed to the negative horizontal shift for Osaka and Los Angeles.
Los Angeles and Osaka are in the Northern Hemisphere and Buenos Aires is int the Southern hemisphere.
Los Angeles y=8.086sin(0.01863t-2.507)+76.08
Osaka y=20.71sin(0.0168t-1.945)+68.97
Buenos Aires y=13.03sin(0.01710t+1.331)+72.38
If there was no shift - like the black graph then The hottest day would be about 1st April.
The southern hemisphere had its hottest day earlier than that. The positive shift number actually moves the graph in the negative direction.
The northern hemisphere has its hottest day elater than that. The negative shift number actually moves the graph in the positive direction.
Here is another graph. I have superimposed a sine wave that has no horizontal shift. It is the black one.
To make it easy to compare I have made the centre line comparable to the others and the period is one year.
Incidental to make the period a year I made the coefficient of t equal to 2pi/364=0.01726
26) When will Los Angeles (red) and Osaka (greeen) have the same daily high temp.
From the graph,
The red and green graphs intersect at about (138,77) and (264,81)
138/364*12 = 4.5494505494505495 That is the middle of April Day 138
264/364*12 = 8.7032967032967033 That is the middle of August, Day 264
27) Logic tells me that they have more chance of all being the same temp in the middle of Spring or Autumn.
So, from the choices, that would be April 25th.
From the graphs I can see that they have the most chance of being the same between day 107 and day 138
Both these days are in April so again it will be April 25th.
28) The vertical shift from 0 degrees for Osaka is 68 degrees (this will be the middle of the temperaure range).
This is less than the other 2 so overall Osaka will be the coldest.
This is answered in probably more detail than you needed NinjaDragon but hopefully you will be able to make sense of it.
:)
Feel free to ask question.
