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September 17, 2014

September 17, 2014

Posted by **Tommy** on Tuesday, July 22, 2008 at 7:35am.

sin (5x) = cos (3x)

sin (6x) sin (x) = cos (3x) cos (4x)

Thanks for your help :)

- Trigonometry -
**drwls**, Tuesday, July 22, 2008 at 7:42amThose are two different equations.

Which one do you want to solve?

- Trigonometry -
**Tommy**, Tuesday, July 22, 2008 at 7:47amI've tried the first one, and i found out that x=45n+11.25 or x=45-180n 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 10:38amNo one helped me ?!

How poor I am ..........

- Trigonometry -
**drwls**, Tuesday, July 22, 2008 at 11:02amI 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 3:10pmsin (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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