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=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 10:38am
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.

## Answer This Question

## Related Questions

- tigonometry - expres the following as sums and differences of sines or cosines ...
- TRIG! - Posted by hayden on Monday, February 23, 2009 at 4:05pm. sin^6 x + cos^6...
- Mathematics - Trigonometric Identities - Let y represent theta Prove: 1 + 1/tan^...
- algebra - Can someone please help me do this problem? That would be great! ...
- trig - Reduce the following to the sine or cosine of one angle: (i) sin145*cos75...
- Calculus 12th grade (double check my work please) - 1.)Find dy/dx when y= Ln (...
- Trigonometry - Solve the equation for solutions in the interval 0<=theta<...
- Trig - Find sin(s+t) and (s-t) if cos(s)= 1/5 and sin(t) = 3/5 and s and t are ...
- Trig - Given: cos u = 3/5; 0 < u < pi/2 cos v = 5/13; 3pi/2 < v < ...
- Precal - I do not understand how to do this problem ((sin^3 A + cos^3 A)/(sin A...

More Related Questions