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Please help me with trigonometry?! URGENT?
T= 5sin(πt/6)+15
T - temperature t- time in hours after midnight on Sunday
1. work out maximum temperature
2. what is the temperature at 4am Monday morning
3. minimum temperature
4. time when temperature is 12 degrees Celsius
Please show all working!
As well as some explanations because I don't know what to do when it comes to word problems.
How do I solve it? That's why I need you to show working.
NB: in case you weren't sure (πt/6) is πt over 6, it is a fraction
With question 4, I'm not clear about how you worked it out. I've tried it on my calculator (set to radians) except I'm not getting the same answers.
Mike - I don't know how you got "πt/6 = arcsin (-0.6 )" could you expand on that please?
especially where you got the -0.6 from
2 Answers
- Anonymous9 years agoFavourite answer
(1).
T = 5 sin (πt/6) + 15
T max if sin (πt/6) = 1
T max = 5 (1) + 15
T max = 20 degrees
(2).
T = 5 sin (π * 4/6) + 15
T = 19.33 degrees
(3).
T = 5 sin (πt/6) + 15
T min if sin (πt/6) = -1
T max = 5 (-1) + 15
T max = 10 degrees
(4).
T = 5 sin (π * t/6) + 15
12 = 5 sin (π * t/6) + 15
t = -(6 asin(3/5))/π
t = 7.22899
or
t = 19.229
- Mike GLv 79 years ago
T= 5sin(Ït/6)+15
1) dT/dt = (5Ï/6)cos(Ït/6) = 0 for maximum or minimum
cos(Ït/6) = 0
Ït/6 = Ï/2 or 3Ï/2
t = 3 (max) or 9 (min)
T = 5sin(Ï/2) + 15 = 20
2) T(4) = 5sin(2Ï/3) + 15 = 19.3
3) T(9) = 5sin(3Ï/2) + 15 = 10
4) -3 = 5sin(Ït/6)
Ït/6 = arcsin (-0.6 ) = 1.2048Ï radians
t = 7.23
7.13 am Monday
