Posted by **Leo** on Monday, July 8, 2013 at 12:40am.

I'm asked to find max and min of: L(t)=12+2.8sin((2pi/365)(t-80).

I find the derivative as:

L'(t)=(5.6*pi/365)*cos[(2pi/365)(t-80)]

but I get lost afterwards.

- Calculus 1 -
**Steve**, Monday, July 8, 2013 at 3:39am
You don't really need any derivatives for this. You know sin(z) has a max od 1 and a min of -1. So, when (2pi/365)(t-80) is an odd multiple of pi/2, sin is 1 or -1, so the min/max of L is 12±2.8

If you want to find the values of t where these extrema occur, then recall that max/min occur when L'=0. So, when does

cos[(2pi/365)(t-80)] = 0?

cos(z)=0 when z is an odd multiple of pi/2. So, for integer values of k, we need

(2pi/365)(t-80) = (2k+1)*pi/2

t-80 = (2k+1) pi/2 * 365/2pi

t-80 = 365(2k+1)/4

t = 80 + 365(2k+1)/4

t = 80±365/4, 80±1095/4, ...

## Answer This Question

## Related Questions

- math - f(x) = 64 + 27cos(2pi/365(x+145)) what would be the period i tried by ...
- Calc..Help Please - A model for the length of daylight (in hours) in ...
- math - how would i multiply 365/365 x 364/365 x 363/365...all the way to 326/365...
- Maths - The sum of three consecutive numbers is 365,find the numbers. X^2+y^2+z^...
- math help plz! - j=6.50% m=Daily(365) f(effective rate)=? f=(1+i)^n =(1+(.0650/...
- triginometry - hi i tried solving this problem but i get the second part wrong...
- math! - j=6.50% m=Daily(365) f(effective rate)=? f=(1+i)^n =(1+(.0650/365))^365...
- MATH, HELP - what is the probability that at least 2 students in a class of 36 ...
- calc - i did this problem and it isn't working out, so i think i'm either making...
- math, help - I need help or hint on the setup: what is the probability that at ...

More Related Questions