Question

Help please. Tigonometry- In what month does the sun rise at 4 a.m. on Cadillac Mountain for the first time? Use this formula to model the sunrise, where t is the time after midnight and m is the number of months after January 1st. (Hint: Substitute t = 4 in the formula and solve for m. Then use the number to find the month. For example, if m = 3.14, the third month, March, is the first month when the sun rises at 4 a.m.).

Answer 1

uh, the answer seems to be in the question here. are you looking for how to get it?

Answer 2

Oh is it? :/ I feel a little dumb now. Lol Sorry I'm replying late, I stepped away from the computer. I'm not even sure what it is that I'm supposed to be solving for, honestly :p

Answer 3

to be honest, I haven't tried to plug the values in, but it seems to be saying that March is the first month where the sun rises at 4am

Answer 4

Oh, that's the hint and that's the example. Not the answer, unfortunately :/

Answer 5

Oh, well it's further than what I got. I appreciate your attempt though (: Thank you!

Answer 6

Ah, how much would it change everything?

Answer 7

I didn't get the first month, but I got a month :
4 = 1.665*sin(pi/6*(m+3)) + 5.485
Now, to isolate m :
(4-5.485)/1.665 = sin(pi/6*(m+3))
sin^-1(-0.89) = pi/6*(m+3)
(-1.097) * 6 / pi = m+3
m = -5.096
Now, I'm assuming that the period of the function is 12, which means that t(-5.096 ) = t(6.904). Now, we got the second month where the sun rises at 4 am, which is June

Answer 8

Mh. I give you props, I would have never found that out Lol.

Answer 9

very little, but I am questioning sin pi/6 (m+3) orders of operation? Hey, m_charron2 that month of June sounds reasonable.

Answer 10

Ohh

Answer 11

I was thinking that sin pi/6 (m+3) was actually sin (pi/6 * (m+3)), since sin's coefficient, 1.665, was already in front of the sin. Makes sense?

Answer 12

I was confused by that sin expression

Answer 13

ok, so for finding the first month, that's where I'm stuck personally... basically, a standard f(x) = sin(x) graph looks like this. The standard period is of 2pi :

now, for this one, the period will be of 12, because we have sin pi/6(x) (don't mind the fact that we suddenly lost the m, we'll get it back a bit later ;-) ), the period is now of 2pi/(pi/6) (I can explain in details how to get to this later if you want)

now, we deal with the m+3. m+3 means that you do a translation on the graph of 3 months to the left. That's now the graph we have so far :

so far so good?