How do you avoid the loss of significance with this expression, sin(x) - tan(x)? I know that subtraction of 2 close real numbers creates large relative error, so how do I restructure this equation in order to get rid of the subtraction sign?

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter5: Polynomial And Rational Functions
Section: Chapter Questions
Problem 27PT: Find the unknown value. 27. y varies jointly with x and the cube root of 2. If when x=2 and...
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How do you avoid the loss of significance with this expression, sin(x) - tan(x)? I know that subtraction of 2 close real numbers creates large relative error, so how do I restructure this equation in order to get rid of the subtraction sign?

I tried using trig indentities: sin(x) - sin(x)/cos(x) = (sin(x)cos(x) - sin(x))/cos(x), but the subtraction sign does not go away.

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