Find the Second Solution for sinx = A | Trigonometry Question

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Homework Help Overview

The problem involves finding the second solution for the equation sin(x) = A, given that x = 7π/23 is one solution. The context is within trigonometry, specifically focusing on the properties of the sine function and its periodicity.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the relationship between the known solution and the properties of the sine function, particularly the identity sin(x) = sin(π - x). There is an attempt to understand the symmetry of the sine function in different quadrants.

Discussion Status

Some participants have provided guidance on using trigonometric identities to find the second solution, while others express uncertainty about the implications of these identities and whether they lead to a different value for A.

Contextual Notes

There is a mention of a missing value for A and the need to find the second solution within the interval [0, 2π]. Participants are navigating the implications of the sine function's symmetry and its effect on the solutions.

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Homework Statement



Suppose that x=7pi/23 is a solution of the equation sinx= A where A is some constant.
Then A must be equal to [blank], and the other solution of the equation in the interval [0,2pi] must be x = [blank].

The Attempt at a Solution



So I've plugged the value into my calculator and found A, but I completely forget Trigonometry. How would I go about finding the second solution?

Thanks
 
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The identity you need to use is sinx = sin([itex]\pi[/itex] - x). Can you see how this shows the symmetry of sinx in the first and second quadrant where two x values give the same A value?
 
Not really, I can see it in my calculator but I don't completely understand it :P and should I be getting a different value?
 
As Bohrok pointed out when x is a solution so too is pi-x
 

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