sin(x)=x/2 ? (1 Viewer)

[denoz]

Just curious really how you would solve this algebraically. Doesn't really have to be this question specifically just something similar eg. sin(2x)=x

 

[onebytwo]

Just curious really how you would solve this algebraically. Doesn't really have to be this question specifically just something similar eg. sin(2x)=x

i dont recall there being any "algebraic" method in particular, but at high school level i recall the only method available are the iterative processes (eg newtons method), but these of course only give you approxiamations, not exact sloutions.
maybe someone can confirm?

 

[watatank]

Not sure ay. I would draw the graph of y = x and see where it meets with sin(2x)

 

[Slidey]

Trig functions are transcendental (as they are actually expressed by exponential functions) and as such, you cannot perfectly solve problems like sin(x)=x.

sin(x) = (e^ix-e^(-ix))/(2i) from memory.

Anyway as you can see it is clearly transcendental and it's even got the imaginary number tucked away in there.

See, cosx+isinx = e^(ix)
e^(ix)-e^(-ix) = isinx+isinx = 2isinx

 

[jb_nc]

http://en.wikipedia.org/wiki/List_o...#Relation_to_the_complex_exponential_function