# Solar Declination

Trigonometry equalities, inequalities and expressions - sin, cos, tan, cot

### Solar Declination

I've been trying to wrap my head around this problem for the last few hours. I have very little math experience so if I could get some help with this it would be great.
The issue is that I've found many problems that claim to give the solar declination. Problem is that when ever I use these equations to find the declination at the equinox the number is not 0. Also the numbers don't seem to follow a slow curved descent or ascent from the highest point 23.45 degrees to the sun's lowest point -23.45. I'm sure the equations are correct and I am doing something wrong. Or interpreting them incorrectly. Here is a website I used

http://www.usc.edu/dept-00/dept/archite ... basic.html

The equation there is:
Declination is calculated with the following formula:
d = 23.45 * sin [360 / 365 * (284 + N)]
Where:
d = declination
N = day number, January 1 = day 1

But if I plug in 81 for N (which is the sping equinox) I get 22.48. I would expect to get 0.
Thanks for any help.
Davros

Posts: 1
Joined: Thu Jan 07, 2016 4:20 pm
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### Re: Solar Declination

You are confusing the units of measurement. The formula requires you to set your calculator to use degrees when computing sin, you have it set on radians.

If N = 81
The formula
$$d = 23.45^\circ\times\sin\left(360^\circ\times\frac{(284+N)}{365}\right)$$
becomes
$$d = 23.45^\circ\times\sin\left(360^\circ\times\frac{(284+81)}{365}\right)$$
$$= 23.45^\circ\times\sin\left(360^\circ\times\frac{365}{365}\right)$$
$$= 23.45^\circ\times\sin\left(360^\circ\right)$$
$$= 23.45^\circ\times 0$$
$$= 0$$

It is not exactly clear on the website that you should be using degrees, since it is not easy to type the symbol $$\;^\circ$$ with a basic text editor. In general people are lazy and don't specify degrees or radians since you can usually work it out from the context and the numbers in the formula (if $$\pi$$ appears somewhere you should probably be using radians, if 360, 180, 90, etc appears then you should probably be using degrees).

Hope this helped,

R. Baber.
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