Intersecting Lines to Solve 2sinx + \sqrt{3} = 0

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To solve the equation 2sinx + √3 = 0 within the interval 0 ≤ x < 360 degrees, the solution yields sinx = -√3/2, resulting in x values of 240 degrees and 300 degrees. The discussion highlights the importance of using special triangles and the CAST rule to find these angles. For the graph of y = 2sinx + √3, the solutions correspond to where the graph intersects the x-axis, specifically at the points 4π/3 and 5π/3. The x-intercepts are identified as the key feature of the graph that indicates the solutions to the equation. Understanding these intersections is crucial for solving similar trigonometric equations.
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a) Use the special triangles and the CAST rule to solve the equation 2sinx + \sqrt{3} = 0 for the domain interval 0 \leq x \geq 360.

b) What feature of the graph, in the form y = asinx + b, would show the solutions?


My Answers:

a) sinx = -\sqrt{3}/2
x = -60 degrees

180 + 60 = 240 degrees
360 - 60 = 300 degrees

b) Can anybody give me a clue as to what this is asking? I have absolutely no idea :(
 
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For b, think about where the graph of y = 2sinx + sqrt(3) crosses the x-axis. I think that's what the problem is getting at.
 
Mark44 said:
For b, think about where the graph of y = 2sinx + sqrt(3) crosses the x-axis. I think that's what the problem is getting at.
This is what I was thinking of as the graph will cross x at 4Pi/3 and 5Pi/3, so I was thinking that the feature to show the solution would be the x-intercepts.

Is this correct? I originally thought this but then was confused by the words "feature of the graph"
 
An x-intercept is a feature of a graph. Again, I think this is what the question is getting at.
 

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