Rearranging two different AsinB(X-C)+D equations to find X values of intercepts

[Volicom]

Rearranging two different AsinB(X-C)+D equations to find X values of intersections

Y=15000sin ((pi/2)(X-2.427397)) + 25000 is one equationY=5000sin((pi/2)X) +6000 is the other

I need to find the intersections of these two graphs using algebra. I have begun by setting them equal, so
15000sin ((pi/2)(X-2.427397)) + 25000 = 5000sin((pi/2)X) +6000

Basically need to rearrange using trigonometry and algebraic rules to find X, which will be the X values of the intercepts. i know that the first 2 X values are 1.239 and 1.4082 and this reoccurs every 4 units of X as they both have a wavelength/period of 4 (e.g. next two intercepts are at 5.239 and 5.4082). No matter how i tackle this, i end up getting stuck :/

3(sin((pi)x/2)cos(2.4pi/2)-cos((pi)x/2)sin(2.4pi/2))-sin((pi)x)/2 = -19/5 Is this correct so far and if so is anyone able to work from there?

 

[Quaid]

Y=15000sin ((pi/2)(X-2.427397)) + 25000

Y=5000sin((pi/2)X) +6000

I need to find the intercepts of these two graphs

i know that the first 2 X values are 1.2391 and 1.4082 and this reoccurs every 4 units of X

Hi Volicom:

"Intercepts" is the wrong word, if you're looking for the X-coordinates of the intersection points of the two graphs.

Can you write the approximate solution-set as follows?

X ≈ 1.2391 + 4N

or

X ≈ 1.4082 + 4N

where N is an Integer


Cheers

 

[Volicom]

Yeah i think using u and v could help make it simpler. And yes i did mean intersections, wrote that late at night and used the wrong word haha. Yep I've got X = 4N + 1.2391 and X = 4N + 1.408, and i have found all the required intersections using the graphing function of my calculator, but i'm pretty sure for top marks I need to be able to rearrange that equation using algebra. Ill have another go at it substituting in u and v.