This is a continuation of a math problem I posted earlier. I'm a little confused by this question.
From your equation, when during the day would the temperature be 30C? (2 marks)
The equation I obtained was: T(t) = 5.9 sin( πt/12 + 7π/6 ) + 27
Any help would be appreciated!
sin(Theta)=3 /5.9
so Theta=arcsin(3 /5.9)= arcsin( 0.508474576)
Theta=PI/6+.01 or theta=PI-PI/6-.01
but Theta=PI*t/12+7PI/6)
so solve for t.
12/PI= t+14 check that
t=12/pi-14 gives negative t
try theta=PI-PI/6-.01
5.9 sin( πt/12 + 7π/6 ) + 27 = 30
sin( πt/12 + 7π/6 ) =3/5.9 = .508447..
set your calculator to radians.
πt/12 + 7π/6 = .53341233 or 2.60818
πt/12 = -3.131779 or πt/12 = -1.057011
t = -11.9625 or -4.037485
now, if you recall, the period of your function was 24 hours, (I helped you with this)
so if we add 24 to each of our answers
so we have t = 12.037 or t = 19.9625
testing:
t = 12.037
T(12.037) = 5.9sin(12.037π/12 +7π/6) = 30
t = 19.9625
T(19.9625) = 5.9sin(19.9625π/12 + 7π/6) + 27 = 30
YEaahhh!
If you make a sketch, you will find a min at t=4, a max at t=16
so the two answers on either side of t=16 make sense.
Thanks once again! You guys are lifesavers
To find when the temperature would be 30°C, you need to solve the equation T(t) = 30.
The equation you provided is: T(t) = 5.9 sin( πt/12 + 7π/6 ) + 27
To solve for t, we can rearrange the equation as follows:
30 = 5.9 sin( πt/12 + 7π/6 ) + 27
Subtracting 27 from both sides, we get:
3 = 5.9 sin( πt/12 + 7π/6 )
Next, we can subtract 3 from both sides to isolate the sine function:
-2.9 = 5.9 sin( πt/12 + 7π/6 )
Now, we divide by 5.9 to undo the multiplication:
-2.9/5.9 = sin( πt/12 + 7π/6 )
To find the angle that has a sine value of -2.9/5.9, we can use the arcsin function:
arcsin(-2.9/5.9) = πt/12 + 7π/6
Now we need to isolate t, so we subtract 7π/6 from both sides:
arcsin(-2.9/5.9) - 7π/6 = πt/12
To solve for t, we multiply both sides by 12/π:
(12/π) * (arcsin(-2.9/5.9) - 7π/6) = t
This expression gives you the value of t when the temperature would be 30°C. Simply substitute the value of the arcsin(-2.9/5.9) and compute the result. Keep in mind that this might involve the use of a calculator or a computer program.