Solve for X: 1.732cos(x)-1.16=sin(x) using Homework Equations

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SUMMARY

The discussion focuses on solving the equation 1.732cos(x) - 1.16 = sin(x) and highlights the incorrect application of algebraic principles during the solution attempt. The correct answer is X = 24.6 degrees, derived from proper manipulation of the equation. A critical error identified was the misapplication of the square of a binomial, where (a - b)² was incorrectly simplified to a² - b². The correct expansion is (a - b)(a - b), which is essential for accurate calculations.

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Homework Statement



Find X?
1.732cos(x)-1.16=sin(x)

Answer: X = 24.6

Homework Equations





The Attempt at a Solution



sin(x) = sqrt(1-cos(x)^2)

1.732cos(x)-1.16=sqrt(1-cos(x)^2)
1.732^2 cos(x)^2 -1.16^2= 1-cos(x)^2
3cos(x)^2-2.3456=1-cos(x)^2
4cos(x)^2=3.3456
cos(x)^2=3.34556/4
x=23.8

There when wrong?
 
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You squared both sides in the first step, right?
Well, the square of 1.732cos(x)-1.16 is not 1.732^2 cos(x)^2 -1.16^2.
You can check it: (a - b)² is not a² - b² but (a - b)(a - b), then open up the brackets...
 
ok thx.. mean i can use (a-b)^2=a^2-2ab+b^2?
 

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