The desert temperature, H, oscillates daily between 36°F at 4 am and 56°F at 4 pm. Write a possible formula for H in terms of t, measured in hours from 4 am.

Question

I thought the answer is -10cos(1/6pi times t) +46
but it got marked wrong.

I thought that the amplitude is 10 because 56-36 divided by 2 is 10.
I got the 46 by doing 56+36 divided by 2.
I got the 1/6pi times t by doing 2pi/12.

Answer 1

Your period is not correct
If the temp is 36° at 4:00am and 56° at 4:00pm
you only have 1/2 a period. Doesn't the temperature have to come back down at 4:00am
so you should have 2π/24 or π/12

so try:
Temp = -10 cos (πt/24) + 46

Answer 2

thank you!!!!
I did mess up the period. I didn't think about it that way. Thank you so much!