Last summer Cooltown, Ontario, experienced several consecutive days of warm temperatures. Below are the temperatures measured for a 24 hour period beginning at midnight and ending the next midnight.
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a and b are very straightforward so I completed those without any issues, c is where I'm running into trouble. I know: a=5.9 d=27 but I'm having difficulty figuring out k and c. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
I am aware: period=2pi/k But I do not know how to find the period with this the values of this graph. Do I assume a period is 24 hours so k=pi/12? Then plug in a point from the data to this equation and find the value of c? | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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trig help!!!
- Thread starter teddy7
- Start date
D
Deleted member 4993
Guest
Time Temp (°C) Time Temp (°C) Time Temp (°C) 0000 23.3 0900 26.3 1800 31.8 0100 22.2 1000 27.8 1900 30.5 0200 21.5 1100 29.5 2000 29.4 0300 21.1 1200 30.6 2100 27.8 0400 21.1 1300 31.8 2200 26.2 0500 21.5 1400 32.5 2300 24.7 0600 22.2 1500 32.9 2400 23.4 0700 23.5 1600 32.9 0800 24.9 1700 32.6
[*=left]Plot the above data. Note: start your vertical scale at a value which takes into consideration the range of the data. For the horizontal scale start with 0 for midnight, then 1 for 1 hour after midnight (0100) and so on. (4 marks)
[*=left]Draw a smooth curve through the points you have plotted. (1 mark)
[*=left]Based on the information from the smooth curve, find an equation for the temperature T in terms of the time t in the form T(t) = a sin(kt − c) + d where a, k, c and d are constants. (4 marks)
[*=left]From your equation predict the temperature at 4:30 pm. (1 mark)
[*=left]From your equation, when during the day would the temperature be 30°C? (2 marks)
a and b are very straightforward so I completed those without any issues, c is where I'm running into trouble. I know:
a=5.9
d=27
but I'm having difficulty figuring out k and c.I am aware: period=2pi/k
But I do not know how to find the period with this the values of this graph. Do I assume a period is 24 hours so k=pi/12?
Then plug in a point from the data to this equation and find the value of c?
Are you supposed to use MS-Excel or some other software to solve this?
No, the table only appeared because that's what happened when I copied and pasted the question.
Are you supposed to use MS-Excel or some other software to solve this?
D
Deleted member 4993
Guest
'd' should be the average of all the temperature numbers.
k = 12/π
Now I would calculate 'c' from all the given points and take the average. If you use a spreadsheet - like Excel - this task will be pretty easy.
k = 12/π
Now I would calculate 'c' from all the given points and take the average. If you use a spreadsheet - like Excel - this task will be pretty easy.