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3. please show full steps 1 the value of cos55180 55...

# Question: please show full steps 1 the value of cos55180 55...

###### Question details

PLEASE SHOW FULL STEPS!

1. The value of cos(55π/180) (55 degrees) can be approximately calculated via the Taylor expansion of cos(θ) about π/4 rad (45 degrees, a known value)

(a) Find the arbitrary Taylor expansion for cos(x) about the unknown value xo to 3rd order (x3 term)

(b) Use the above to approximate the value of cos(55π/180), by expanding about the known angle π/4. That is find the Taylor expansion of cos(θ) about 45 degrees (xo=π/4), and then evaluate at x = 55π/180 (55 degrees). Note that the Taylor expansion is evaluated in radians not degrees (i.e π/4, and 55π/180 are the two correct values).

(c) (PYTHON programming!!!) Plot the difference between your expansion about 45 degrees and the actual values over the a range of angles from 30 to 60 degrees. (Submit your code, and the plot)

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