Write the cubic term for the Taylor series expansion of f(x) = sin(x) at c = pi/4

I did the work, can you please check for me whether my work is right?

Step-by-step explanation:

Close, the second term should have an exponent of 1.

f(x) = f(c) + f'(c) (x−c)¹/1! + f''(c) (x−c)²/2! + f'''(c) (x−c)/3!

f(x) = 1/√2 + 1/√2 (x−π/4) − 1/(2√2) (x−π/4)² − 1/(6√2) (x−π/4)³

explanation:

step-by-step explanation:

multiplication is multiplication.   it might feel harder depending on what level of math you are in, but generally it will be the same old stuff, while implementing some new concepts and methods of solving work.