# Solve for T

1. Sep 25, 2008

### ally79

This equation is killing me, Sin(2T) = (625/4) x sin(40)

I have need to solve it for T where T is the angle. However I either end up getting an error or an angle that is less than 1 degree which i know is wrong.

Initially i tried doing the 625/4 x sin 40 which gave me 100.44

So i had Sin(2T) = 100.4

then tried to take the Sin of both sides but get an error on my calculator.

Please help me, it seems so simple to me but i just cant get my brain to work

2. Sep 25, 2008

### dodo

Maybe it does not have a solution. This other equation, sin(x)=2, doesn't have a solution either, since the range of the sin function is [-1,1].

The only possibility I see is that your angles are not in degrees (nor in radians either), but in some hypothetical and very small unit. For example, suppose "40" is not in degrees, but in 1000ths of a degree, in "millidegrees". Then (625/4) x sin(40 millidegrees) would be in the range [-1,1].

P.S.:
Is there a chance of some error in the "625" number? Because if it were close to 6.25 (6 point 25), (actually, if it were just a bit smaller than 6.25), then 6.25/4 x sin(40) would be very close to 1.

Last edited: Sep 25, 2008
3. Sep 26, 2008

### HallsofIvy

Staff Emeritus
You mean, I presume, take the arcsine rather than Sin. Yes, you will get an error for that: for any number x, sin(x) is between -1 and 1. No matter what T is, sin(2T) must be between -1 and 1. There is NO T such that sin(2T) is equal to 100.4.

Where did you get "sin(2T)= 625/4 x sin(40)"?

(One possiblity, though I am reluctant to mention it, is that you are dealing with complex numbers. sin(2T)= (e2T- e-2T[/itex])/2 can be equal to 100.4 if T is an imaginary number. Surely that's not what you want?)