What the heck is "tan"?!

I'm taking an Astronomy class which starts on the 27th of September. Since I'm terrible at Math, and frankly got anxious..I cracked my Astronomy book only to find math problems. Who would have thought? Anyway, I am asking you all for help.

In the chapter discussion of "Observational Measurements Using Angles" we are told and given the following formula: "

In general, the physical diameter of an object can be calculated from the equation:

physical diameter=distance x tan (angular diameter)

where tan (angular diameter) means the tangent of the angle denoted "angular diameter" In the Moon's case, using a measured distance of 384,400km and an angular diameter of 1/2¡ (<--degree), we find the diameter to be roughly 3350km.

Now...I realise for other people, they might know what the heck this means, but I for the life of me CANNOT replicate that answer. I typed in 384400 x tan (just pressing the tan key!), I've typed in 384400 x tan(180)...basically, what is tan? And what is the number for it, or how do I find it? I'm feeling VERY down on myself about this.

Please, any help would be appreciated!!

Hello Sarah,

1st, relax and let`s backtrack a bit. Keeping it simple, (I hope), let`s take another look at the ex. given in the book. In that ex., the book means that the moon`s angular diameter is 1/2 of a degree or(1/2)*.

Also for the purpose of simplicity, let`s change the fraction 1/2 into an equivalent decimal which can be used more easily on your calculator,

Then we get 1/2 =.5

Now punch in .5 on your calculator and take the tangent of that. Then multiply this answer by 384,400 and you should get roughly 3350 just like the book states!

Other problems like this work out the same way. Take the tangent of the angular diameter converted to an equivalent decimal just like we did when we changed 1/2 to .5 and took the tangent of .5 on the calculator. Then multiply that answer by the distance to that object just like we multiplied that answer by the distance to the moon which is 384,400km. This will give you the physical diameter of the object just like it gave us an answer of roughly 3,350km. for the physical diameter of the moon.

In brief and perhaps more simply then, the book is saying to use this formula,

tang of angular diameter in degrees x distance to object in km. = object`s physical diameter in km. or in the moon ex.,

Tang. .5 x 384,400 = 3,350, (roughly),

Hope This Helped, 8) and let us know if you still don`t understand it. If you have any other questions, feel free to ask!!! 8)

Good Luck!!!