Posted by Tommy on Tuesday, July 22, 2008 at 7:35am.
Find the general solution of the following equation.
sin (5x) = cos (3x)
sin (6x) sin (x) = cos (3x) cos (4x)
Thanks for your help :)

Trigonometry  drwls, Tuesday, July 22, 2008 at 7:42am
Those are two different equations.
Which one do you want to solve?

Trigonometry  Tommy, Tuesday, July 22, 2008 at 7:47am
I've tried the first one, and i found out that x=45n+11.25 or x=45180n but i don't know if i am correct or not.
The second one I just cant do it.

Trigonometry  Tommy, Tuesday, July 22, 2008 at 10:38am
No one helped me ?!
How poor I am ..........

Trigonometry  drwls, Tuesday, July 22, 2008 at 11:02am
I could write both equations in terms of sines and cosines of x, but they become an incredible mess. There may be an elegant solution to either, but don't see it.

Trigonometry (shortcut)  drwls, Tuesday, July 22, 2008 at 3:10pm
sin (5x) = cos (3x)
That relationship is true if the argument of the sin term is y and the argument of the cos term is pi/2  y.
Let
5x = y, and
3x = pi/2 y
Now solve for y.
15x = 3y
15x = 5 pi/2 5y
0 = 8y  5 pi/2
y = 5 pi/16 = 56.25 degrees is an answer
There may be another answer as well, since the
sin a = cos b
relationsip is also true whenever the argument of the sin term is y and the argument of the cos term is 3 pi/2 + y.
So let
5x = y
3x = 3 pi/2 + y
15x = 3y
15x = 15 pi/2 + 5 y
2y = 15 pi/2
So y = 15 pi/4 = 675 degrees, or 315 degrees, or +45 degrees is another answer.
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