Question 551745: Consider the equation sin(x)=-square root of (3)/2. how many values of theta between 0 degrees and 360 degrees will make this true. The answer is 2. How do you get 2?
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Consider the equation sin(x)=-square root of (3)/2. how many values of theta between 0 degrees and 360 degrees will make this true. The answer is 2. How do you get 2?
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Referring to a unit circle, one cycle or 360º is divided into four quadrants. Note that the sin function, or the vertical leg of the reference angle is positive in quadrants I and II, and negative in quadrants III and IV. This is why two different angles in quadrants I and II would give the same positive sin value and two different angles in quadrants III and IV would give the same negative sin value.
For your given example, if sin(x)=-√3/2, x=240º and 300º. If sin(x)=√3/2, x=60º and 120º.
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Note of caution: when working with inverse functions, only one angle is the answer for a given sin value because of their restrictive domains. For example, domain for arcsin function is between -90º and 90º, that is, the angle is in either quadrant I or IV. For example, arcsin(-√3/2)=300º but not 240º
When solving for angles, you must make the distinction between regular equations and inverse functions.
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