sin2x=cos3x, solve for x

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- November 18th 2006, 02:26 PM #1

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- November 18th 2006, 02:34 PM #2

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- November 18th 2006, 02:36 PM #3

- November 18th 2006, 03:02 PM #4

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Hello, lexmex1546!

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

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 . . .

- November 18th 2006, 05:55 PM #5
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