finding amplitude and period based off of a function.

Question

The desert temperature, H, oscillates daily between 34ºF at 5am and 74ºF at 5pm. Write a possible formula for H, measured in hours from 5am. Use the form H = Acos(Bt) + C.

so I got

A=20

b=2pi/12

and C=20

but my answers were wrong and I don't know why. For amplitude wouldn't you subtract the values and take the half of it? and for B wouldn't it be 2pi over b? for C I don't know I just guessed. Please help me, I am so confused.

Answer 1

Dhiradj, you are making this too diificult! Let's do this thing!

 

You found the amplitude correctly.

 

Remember that a perios ends when the cycle starts over again. It starts again at 5 am, 24 hours later, so our B = 2pi/24 = pi/12.

 

C is the vertical shift. Normal cosx starts at 1 and goes down to -1, and the middle is 0. Halfway between 34 and 74 is (74 + 34)/2 = 54.

 

Lastly, I said cosx starts at 1 and goes down to -1. We are starting at 34 and going up, soooooo our final answer should be...

 

H = -20cos(pi/12) + 54

 

Hope this helps!