Finding polynomial approximations of a sine wave

1. How do you approximate a sine wave?
2. How do you approximate sine with Taylor series?
3. Can a sine function be a polynomial?

How do you approximate a sine wave?

Bhaskara's Approximation Formula: sin(θ◦) ≈ 4θ(180 − θ) 40500 − θ(180 − θ) , for 0 ≤ θ ≤ 180.

How do you approximate sine with Taylor series?

In order to use Taylor's formula to find the power series expansion of sin x we have to compute the derivatives of sin(x): sin�(x) = cos(x) sin��(x) = − sin(x) sin���(x) = − cos(x) sin(4)(x) = sin(x). Since sin(4)(x) = sin(x), this pattern will repeat.

Can a sine function be a polynomial?

and F (x) = f(x). Unfortunately, not all functions are polynomials. For example, although it would take some time to prove this, sin(x) is not a polynomial function (can you find real numbers a0,a1,...,an such that sin(x) = a0 + a1x + ··· anxn?).