Make x the subject of the equation.

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Homework Help Overview

The problem involves manipulating a trigonometric equation to isolate the variable x. The specific equation given is sin(5x-24)=0.6, which falls under the subject area of trigonometry.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the steps taken to isolate x, including the use of the inverse sine function. Some question the implications of the arcsin function's range and the existence of multiple solutions.

Discussion Status

There is an ongoing exploration of the problem, with participants confirming the algebraic manipulation while also raising questions about the nature of the solutions and the constraints imposed by the arcsin function.

Contextual Notes

Participants note that the equation may yield an infinite number of solutions, depending on the periodic nature of the sine function, and discuss the implications of measuring angles in radians.

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Homework Statement



Make x the subject of the formula

sin(5x-24)=0.6

Homework Equations



sin(5x-24)=0.6

The Attempt at a Solution



sin(5x-24)=0.6
5x-24=sin^-1(0.6)
x=(sin^-1(0.6)+24)/5
 
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You had it right I believe, what exactly is your question?

sin(5x-24) = 0.6

5x - 24 = arcsin(0.6)

5x = 24 + arcsin(0.6)

x = [24 + arcsin(0.6)] / 5

X = ~12.174
 
Or, if (5x-24) is measured in radians, x is about 4.93.
 
There should be an infinite number of solutions, shouldn't there? Remember that the range of the arcsin function is only [-π/2, π/2].
 

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