Many applications use the following "small angle" approximation for the sine to obtain a simpler model that is easy to understand and analyze. This approximation states that sin x= x, where x must be in radians. Investigate the accuracy of this approximation by creating three plots (use he subplot function to group them); 1. Plot sin x and x versus x for 0 sxs 1. [Hint: use an increment for x of 0.01]. 2. Plot the approximation error sin x-x versus x for 0 sxs 1. [Hint: use an increment for x of 0.01). 3. Plot the relative error [sin(x) - x)/sin(x) versus x for 0 sxs 1. [Hint: use an increment for x of 0.01).

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
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Many applications use the following "small angle" approximation for the sine to obtain a simpler model that is easy to
understand and analyze. This approximation states that sin x= x, where x must be in radians.
Investigate the accuracy of this approximation by creating three plots (use he subplot function to group them):
1. Plot sin x and x versus x for 0 sxs 1. [Hint: use an increment for x of 0.01].
2. Plot the approximation error sin x-xversus x for 0 sxs 1. [Hint: use an increment for x of 0.01].
3. Plot the relative error [sin(x) - x)/sin(x) versus x for 0 sxs 1. [Hint: use an increment for x of 0.01).
How small must x be for the approximation to be accurate within 5%? Use the plot to estimate a value and store your answer in
a variable named x 5.
Transcribed Image Text:Many applications use the following "small angle" approximation for the sine to obtain a simpler model that is easy to understand and analyze. This approximation states that sin x= x, where x must be in radians. Investigate the accuracy of this approximation by creating three plots (use he subplot function to group them): 1. Plot sin x and x versus x for 0 sxs 1. [Hint: use an increment for x of 0.01]. 2. Plot the approximation error sin x-xversus x for 0 sxs 1. [Hint: use an increment for x of 0.01]. 3. Plot the relative error [sin(x) - x)/sin(x) versus x for 0 sxs 1. [Hint: use an increment for x of 0.01). How small must x be for the approximation to be accurate within 5%? Use the plot to estimate a value and store your answer in a variable named x 5.
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