Question

Trigonometry!
Is there any fast function for finding solutions in a certain interval?
Ex.
x = 150 + n * 360 (This derives from solving an trigonometric equation)
and 1000 < x < 1300

How can check this without testing every n?
n is an integer.

Answer 1

Not exactly sure what you're asking...if you have a solution to a trig equation that is in the form x=a + 2*pi*n, where n is an integer, it just means that the answer includes all angles repeated every 2pi units (or 360 degrees, since 2pi is in radians). In other words, if you have to find x for which cos(x) is sqrt(3)/2 and sin(x) is 1/2, it's 30 degrees only if you're restricted to x in [0, 360), but if you're open to all real numbers, it's 30 degrees, 390, 750, etc, since those values repeat every 360 degrees (one turn around the unit circle). Make sense?

Answer 2

Yes I see what you mean. And I'm working with degrees instead of radians but I understand.
What I want to know is, when you get the solutions:
30, 390, 750 etc
And you want an answer that is say between 360 and 720
360 < x < 720
Then 390 would be the answer.
But what is these where huge numbers?
360 * 10^10 < x < 360 + 360 * 10^10
This would take forever to check by increasing n right?

Answer 3

Yeah, in general it would take a long time. I mean, you could write an equation like 30+
360x (30 is your first answer, plus all multiples of 360)=360*10^10, and then get what multiply of 360 you'd need to add to get to one end of your range, and do the same thing to the other end, and that will get you an approximate range that you're looking at. Of course, if the range of answers you need is big enough, it will take a while regardless. This also isn't trigonometry at this point...it's just algebra and reasoning.

If you gave me an example problem from your book that is the type that you're having problems with, I can try to be of more help.

Answer 4

Okey, thank you!
The problems in the book have fair ranges. But I was just curious about how it would apply to larger ranges.

Answer 5

Ok, usually problems with ranges that big (like the ones you illustrated) are rare in trig problems, at least at the h.s./college level. Good luck!