Use procedure to find Taylor polynomial of degree 4 for sinx with a=pi/4.

Use procedure to find Taylor polynomial of degree 4 for f(x) = sinx with a = pi/4. Use the result to approximate sin 50º.

Thanks for help!

Using the definition:
f(x) = sin x ==> f(π/4) = √2/2
f '(x) = cos x ==> f '(π/4) = √2/2
f ''(x) = -sin x ==> f ''(π/4) = -√2/2
f '''(x) = -cos x ==> f '''(π/4) = -√2/2
f ''''(x) = sin x ==> f ''''(π/4) = √2/2

Hence, sin x
≈ √2/2 + (√2/2)(x - π/4) - (√2/2)(x - π/4)^2/2! - (√2/2)(x - π/4)^3/3! + (√2/2)(x - π/4)^4/4!.

Since this is a series in radians, note that 50º = 50π/180 = 5π/18.
Now, substitute x = 5π/18 for the desired approximation.

I hope this helps!