Sum and difference with radians.

[Tyrion101]

I think I understand the basic ideas of the sum and difference formulas, I just don't get how to break down say, pi/7 into a form that could be worked with. I could convert it to a degree then back again once I have my answer, but that seems like a lot more work than is necessary. If it were 100 degrees I'd just find some form of 100 degrees that I knew had an angle that was on the unit circle. 100 degrees doesn't seem to work very well but you get what I'm attempting to ask here. Also, can it only work if it is an angle that can be divided evenly like 120 degrees?

 

[jedishrfu]

I don't understand your difficulty.

Are you saying that you don't understand pi/3 as a radian measure and so (1/3)pi + (1/2)pi = (5/6) pi is something in fractions you can't handle?

 

[SteamKing]

I think I understand the basic ideas of the sum and difference formulas, I just don't get how to break down say, pi/7 into a form that could be worked with. I could convert it to a degree then back again once I have my answer, but that seems like a lot more work than is necessary. If it were 100 degrees I'd just find some form of 100 degrees that I knew had an angle that was on the unit circle. 100 degrees doesn't seem to work very well but you get what I'm attempting to ask here. Also, can it only work if it is an angle that can be divided evenly like 120 degrees?

Well, there is an angular measurement system made for the math-challenged and civil engineers:

http://en.wikipedia.org/wiki/Gradian

The angular unit is called the 'gon', but it also used to be known as the 'grad' or 'gradian'. There are 400 grads in one revolution of a circle, or 100 grads in a right angle.
Calculators are often equipped to calculate trig functions using angles measured in degrees, radians, or grads, usually by flipping a switch or setting a special mode.

It's still not clear what your original complaint is about. If you want to calculate sin (π/7), you put your calculator into radian mode, calculate π/7, and take the sine of that angle.

 

[lurflurf]

All angles are on the unit circle. Maybe you are talking about constructable angles? An angle m*pi/n in lowest terms is constructable if and only if the factors of n are limited to any power of 2 and Fermat primes (known ones being 3, 5, 17, 257, 65537) at most once each. In trigonometry class one tents to consider multiples of pi/15/2^k. Note that pi/ 7 and 100 degrees are not constructable.