solve 2x+1 = 3sin(x/2) (1 Viewer)

[Layzie_Bone]

solve 2x+1 = 3sin(x/2)
i have noe idea how to do this
mayb some help plz?

 

[shafqat]

solve 2x+1 = 3sin(x/2)
i have noe idea how to do this
mayb some help plz?

this isnt an hsc question. are u sure there wasnt more information, like find how many solutions maybe, rather than the solutions themselves?

 

[Layzie_Bone]

Find x?
thats all i got

 

[shafqat]

in that case all u can do is accurately graph them, find the point of intersection and give an estimate for x

 

[Layzie_Bone]

so simple, yet it skipped my mind...

 

[grendel]

how about rewriting 2x+1 = 3sin(x/2) as 3sin(x/2)-2x-1=0 and using the halving the interval method to approximate the answer.

still only an approximate answer but after many iterations could be reasonably accurate.

 

[jm1234567890]

yeah, unfortunately the only answer to that will be an estimate.

 

[Slidey]

0=3sin(x/2)-2x-1
y'=3/2.cos(x/2)-2

test x=-1:
a=-1-(-.45)/(-.63)=-1.71
b=-1.71-(0.1)/(-1)=-1.61
c=-1.61-(.06/-.95)=-1.54
d=-1.54-(-.01/-.91)=-1.55

So it is at about x=-1.55

 

[blackfriday]

yeh all you can do is use newton's method or halving the interval. it is impossible to solve for x.

 

[acmilan]

The closest estimate I managed to get for the graph of y = 3sin(x/2) - 2x - 1 was -1.549 when y = -2.70181x10^-6 (damn near 0!)