sin (pi.x/3) = 1/25.x^2-1

[vjekobalas]

sin (pi.x/3) = 1/25.x^2-1

I'm not sure how to find the values.
If I take sin (pi.x/3), period = 2pi/(pi/3) = 6
This gives a sine wave starting at 0,0, amplitude 1, with one period ending at 0,6
and the period before that starting at -6,0 to 0,0

for the parabola 1/25.x^2 -1, using
x1,2 = -b+-sqrt(b2 -4ac), x1,2 is 5& -5, and when x=0, y=-1
i.e parabola starting at 0,-1 , going through 0,-5 and 0,5

and the two can be roughly plotted, but how do you
find the exact coordinates of intersection ?

 

[stapel]

sin (pi.x/3) = 1/25.x^2-1

I'm not sure how to find the values.

"How to find the values" of what? What is the meaning of the decimal-point dots in this equation? What were the instructions for this equation? What are you trying to accomplish?

If I take sin (pi.x/3), period = 2pi/(pi/3) = 6
This gives a sine wave starting at 0,0, amplitude 1, with one period ending at 0,6 and the period before that starting at -6,0 to 0,0

for the parabola 1/25.x^2 -1, using x1,2 = -b+-sqrt(b2 -4ac), x1,2 is 5& -5, and when x=0, y=-1 i.e parabola starting at 0,-1 , going through 0,-5 and 0,5

Um... what? What, exactly, are you attempting to do?

Please be complete. Thank you!

 

[vjekobalas]

sorry the dot is not needed

how would you find the solution i.e. points where sin (pi.x/3) = 1/25x^2-1
i.e. I can draw the graphs of the parabola and sin curve but how would
I be able to work out the points of intersection

 

[stapel]

sorry the dot is not needed

how would you find the solution i.e. points where sin (pi.x/3) = 1/25x^2-1

If "the dot is not needed", then why is it still included?

If you are attempting to find an algebraic solution (that is, a solution worked out with algebra-based steps, leading to an exact value), then I doubt that this is possible. The right-hand side of the equation is algebraic; the left-hand side is transcendental. Your best bet will be numerical methods.

If you meant something else, kindly please reply with answers to the questions previously posed to you. Thank you!

 

[Steven G]

sin (pi.x/3) = 1/25.x^2-1

I'm not sure how to find the values.
If I take sin (pi.x/3), period = 2pi/(pi/3) = 6
This gives a sine wave starting at 0,0, amplitude 1, with one period ending at 0,6
and the period before that starting at -6,0 to 0,0

for the parabola 1/25.x^2 -1, using
x1,2 = -b+-sqrt(b2 -4ac), x1,2 is 5& -5, and when x=0, y=-1
i.e parabola starting at 0,-1 , going through 0,-5 and 0,5

and the two can be roughly plotted, but how do you
find the exact coordinates of intersection ?

I agree with what you are saying when it comes to finding intersecting points. Unless the two functions are linear, at best you get an approximation. I too do not think that you can solve your equation algebraically.

 

[vjekobalas]

OK, thanks - that clears it up.