Find the taylor series for f(x)=sin(x) centered at c=π/2.sin(x)=∑ n=0 [infinity]on what interval is the expansion valid? give your answer using interval notation.

sinx =1-\frac{1}{2} (x-\frac{\pi}{2} )^2+\frac{1}{24} (x-\frac{\pi}{2} )^4-\frac{1}{720} (x-\frac{\pi}{2} )^6+\frac{1}{40320} (x-\frac{\pi}{2} )^8+...

Step-by-step explanation:

given that f(x) = sin x

we have to find the Taylor series for that

and so on.

i.e. 2nd, 4th, 6th terms would be 0

and also 1st, 5th, 9th terms would be positive for f value and 3rd, 9th,... would be negative

Using the above we can write Taylor series as

This is valid for all real values of x.

x ∈

10000

step-by-step explanation: divide by 2,