Chapter 7, Problem 33P

To determine

(a)

To write:

A user-defined function that calculates $\sin x$ using Taylor’s series expansion such that $\text{y}=\text{cosTay(x)}$ is used as function name and arguments; a user-defined function such that if the angle is larger than $360°$ or smaller than $–360°$ then the Taylor series will be calculated using the smallest number of terms; a code that calculates $\cos 67°$ using the above function and compare this value from the value obtained by using MATLAB’s built-in $\text{sind}$ function.

To determine

(b)

To write:

A user-defined function that calculates $\sin x$ using Taylor’s series expansion such that $\text{y}=\text{cosTay(x)}$ is used as a function name and arguments; a user-defined function such that if the angle is larger than $360°$ or smaller than $–360°$ then the Taylor series will be calculated using the smallest number of terms; a code that calculates $\cos 200°$ using the above function and compare this value from the value obtained by using MATLAB’s built-in $\text{sind}$ function.

To determine

(c)

To write:

A user-defined function that calculates $\sin x$ using Taylor’s series expansion such that $\text{y}=\text{cosTay(x)}$ is used as function name and arguments; a user-defined function such that if the angle is larger than $360°$ or smaller than $–360°$ then the Taylor series will be calculated using the smallest number of terms; a code that calculates $\cos \left(-80°\right)$ using the above function and compare this value from the value obtained by using MATLAB’s built-in $\text{sind}$ function.

To determine

(d)

To write:

A user-defined function that calculates $\sin x$ using Taylor’s series expansion such that $\text{y}=\text{cosTay(x)}$ is used as function name and arguments; a user-defined function such that if the angle is larger than $360°$ or smaller than $–360°$ then the Taylor series will be calculated using the smallest number of terms; a code that calculates $\cos 794°$ using the above function and compare this value from the value obtained by using MATLAB’s built-in $\text{sind}$ function.

To determine

(e)

To write:

A user-defined function that calculates $\sin x$ using Taylor’s series expansion such that $\text{y}=\text{cosTay(x)}$ is used as function name and arguments; a user-defined function such that if the angle is larger than $360°$ or smaller than $–360°$ then the Taylor series will be calculated using the smallest number of terms; a code that calculates $\cos 20000°$ using the above function and compare this value from the value obtained by using MATLAB’s built-in $\text{sind}$ function.

To determine

(f)

To write:

A user-defined function that calculates $\sin x$ using Taylor’s series expansion such that $\text{y}=\text{cosTay(x)}$ is used as function name and arguments; a user-defined function such that if the angle is larger than $360°$ or smaller than $–360°$ then the Taylor series will be calculated using the smallest number of terms; a code that calculates $\cos \left(-738°\right)$ using the above function and compare this value from the value obtained by using MATLAB’s built-in $\text{sind}$ function.