sin2x=cos3x, solve for x

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- Nov 18th 2006, 03:26 PMlexmex1546help
sin2x=cos3x, solve for x

- Nov 18th 2006, 03:34 PMThePerfectHacker
- Nov 18th 2006, 03:36 PMtopsquark
- Nov 18th 2006, 04:02 PMSoroban
Hello, lexmex1546!

Here's a "cute" way to approach this problem . . .

Quote:

Solve for

. . we see that and are angles in the*same right triangle*. . .

Code:`*`

* *

* 3x *

* *

* *

* *

* 2x *

* * * * * * * *

Therefore: .

Of course, this is__not__a complete solution . . .

- Nov 18th 2006, 06:55 PMtopsquark
The hard way.

Thus:

Pull everything to the LHS and factor the common cos(x):

So either or

For the sin solution, use the quadratic formula to find:

So

So the whole solution set in the domain will be x = from the solution and x = from the sine solution. These may be easily seen to be the same solutions as ThePerfectHacker gave you, only from a much messier derivation.

-Dan