Find all solutions of sin 2theta = 2 , where theta is an angle measured in degrees.

Answer 1

Sorry Jillian A.,

Since the sin function only runs (for real values of theta) between +/- 1, there are NO solutions to your problem in the real domain. Of course, in the complex domain for θ (if that's not too bizarre a concept for you?), you might be able to eke out solutions.

Let's see: e^(iθ) = cos(θ) + i*sin(θ)

Then if we let θ = ix + y then

crank on through with cos (sum of angles), sin (sum of angles) formulas etc. to: (if I haven't made any math errors along the way?)

[cos(x)cos(y) + (e^(-x)-e^(x))cos(y)/2] + i * [cos(x) + ((e^(-x)-e^(x)) * sin(y)/2] = 2

That's a simultaneous equation in x and y, the real part must = 2, and the imaginary part must = 0.

If there ARE solutions, you might discover them graphically, or with a little spreadsheet (recommend separate sheets for the two components, so that the patterns can be eyeballed quickly!) for x, y and the two required portions (real and imaginary components). Then remember to correct for the original 2θ factor!

-- Cheers, -- Mr. d.

Answer 2

The range of sin function is -1 to 1

So Sin 2θ = 2 has no solution