Sarah Word Problem

She also asked to sate the amplitude , frequency , period , domain , range , phase shift , and reflection
Word problem:
The average monthly temperature of a town can be modelled by the function T(t)= 14.6 sin 0.5( t-1)+9.15. where T is the tempertaure in degrees and t=0 represents january first, t= 1 represents febrauary 1 etc...lkd
a) which month is the average monthly temperature the highest?the lowest?
b) use the model to predict when temp is 0?
c) when is the temperature 20?

T(t)= 14.6 sin 0.5( t-1)+9.15

amp=14.6
freq=.5
Phase shift= .5*-1 = -.5
Period=2pi/.5=4pi or approx 12
Domain= Infinity the sin graph goes on forever on the x-axis
Range= 9.15 then add 14.6 and get a maximum of 23.75 and then 9.15-14.6 and you get minimum of -5.45
reflection= ?


Since you are being asked the month with the maximum temp. You need to say

23.75=14.6 sin 0.5( t-1)+9.15

then you solve for t

subtract 9.15

14.6 =14.6 sin 0.5( t-1)

divide by 14.6

1= sin 0.5(t-1)

sin inverse of 1 = 0.5(t-1)

1.57 = 0.5(t-1)

3.14 = t-1

t=4.14

The maximum temperature is in May as May is equal to 4


When is the temperature 20 or 0

20=14.6 sin 0.5( t-1)+9.15

t= 2.67 or Middle of March

0=14.6 sin 0.5( t-1)+9.15

Solve them the same way as I showed above.