Sum of trig solutions

Identity · 2007-12-08 01:46:06

For the equation sin(2x) = 1, what are the sum of the solution in the interval [0, 4pi]?

I got 14pi but the answers say 7pi, thanks

mathsyperson · 2007-12-08 03:03:39

I get 7π as well.

If the equation was sin(x) = 1, then the solution would be x = π/2 + 2kπ, with k being an integer.

Therefore, in this case 2x = π/2 + 2kπ, and so x = π/4 + kπ.

The interval is [0,4π], so the set of solutions is {π/4, π+π/4, 2π+π/4, 3π+π/4}.

Summing the wholes gives 6π, and there are four quarters which gets you another one, so the answer is 7π.

Identity · 2007-12-08 03:32:07

Thanks, mathsyperson

I think you're missing a few solutions, since the period is only

.

This is my solution, is it right?

As

,

So the solutions are

All the

's cancel out, so the sum of the roots are:

Last edited by Identity (2007-12-08 03:46:19)

mathsyperson · 2007-12-08 04:31:11

You're counting each solution twice. π/2 = π - π/2, for example.

Math Is Fun Forum