Question

The temperature in an air conditioned home can be modelled by the function:
C(t)= 1.5sin(pi/12(t+6))+20

where t is the time in minutes after the air conditioner turns on, and C is the temperature inside the home in degrees Celsius.

The number of minutes that the temp takes to reach 19 degrees celsius for the first time after the AC turns on is _______?

Answer 1

19=1.5sin(pi/12(t+6))+20

Answer 2

how do I solve for t?

Answer 3

I did it on my graphing calculator and got 8.79 minutes, but thats cheating. ;)

Answer 4

I'm guessing you just do the opposite of PEMDAS.
\[19 = 1.5\sin[\frac{π}{12}(t + 6)] + 20\]\[-1 = 1.5\sin[\frac{π}{12}(t + 6)]\]\[-2/3 = \sin[\frac{π}{12}(t + 6)]\]\[\sin^{-1} (-2/3) =\frac{π}{12}(t + 6)\]

Answer 5

\[1.5\sin(\frac{\pi}{12}(t+6))+20=19\]
\[1.5\sin(\frac{\pi}{12}(t+6))=-1\]
\[\sin(\frac{\pi}{12}(t+6))=-\frac{2}{3}\] then a calculator

Answer 6

how come you don't move the 1.5 over to the other side before the 20?

Answer 7

When reversing PEMDAS, you start with addition/subtraction, then you do multiplication/division

Answer 8

THe only reason you would divide first is if the 20 were within the parentheses.

Answer 9

hmm, interesting, don't know why I was never taught that.

Answer 10

thanks guys!

Answer 11

No Problem :)

Answer 12

@baldymcgee6 did u get 8.79 minutes after solving?
im getting a negative value... .not sure