Question

What would be steps and reason to answering the following question? Also thank you ahead for helping me understand the question. :)

approximate the value of sin(0.8).

1. Find the Maclaurin series for sin(x).
   1. Do we have enough information to use right triangles to estimate sin(0.8)? Why?
   2. Estimate sin(0.8) using values of sin(x).
   3. Estimate sin(0.8) using the graph of y = sin(x) from the graph of y = sin(x), −2π ≤ x ≤ 2π.
   4. Estimate sin(0.8) using the 5th degree Taylor polynomial for sin(x) at a = 0 ( Using either the Taylor polynomial up to n = 5 or the Taylor polynomial up to the x⁵ term).
   5. Find the error bound from the Alternating Series Estimation Theorem (using the next nonzero term of the Maclaurin series), and explain what it tells us about the actual value of sin(0.8).

Answer 1