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# sin(x) infinite series Watch

1. I know that sin(x) = x - (x^3)/3! + (x^5)/5! ....

But what I don't understand is how this relates to a triangle (i.e. opposite/hypotenuse). Can anyone shed some light?
2. (Original post by Robbie!)
I know that sin(x) = x - (x^3)/3! + (x^5)/5! ....

But what I don't understand is how this relates to a triangle (i.e. opposite/hypotenuse). Can anyone shed some light?
It comes from the Maclaurin Series of sin(x), which is a generalised Taylor Series around x = 0.

The link has a helpful graph illustrating what the Taylor Series actually does.
3. (Original post by Robbie!)
I know that sin(x) = x - (x^3)/3! + (x^5)/5! ....

But what I don't understand is how this relates to a triangle (i.e. opposite/hypotenuse). Can anyone shed some light?
This infinite series relates to the value of sinx and does not to a triangle.
The value of sinx is a ratio in a triangle - more generally it is the y coordinate
of the unit vector of i rotated around the origin with an any real angle (clockwise or counterclockwise (-/+) in the Cartesian coordinate system.
So this value maybe between -1 and 1, and mostly is an irrational number.

The series means we can approache this value by infinite series of given rational (maybe real) terms, so we can calculate the value of sin x with any accuracy, using
so many terms as it is needed.

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