If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Set equal to and solve for .
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Set equal to .
Solve for .
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Take the inversesine of both sides of the equation to extract from inside the sine.
Simplify the right side.
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The exact value of is .
The sinefunction is positive in the first and secondquadrants. To find the secondsolution, subtract the reference angle from to find the solution in the secondquadrant.
Subtract from .
Find the period of .
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The period of the function can be calculated using .
Replace with in the formula for period.
The absolute value is the distance between a number and zero. The distance between and is .
Divide by .
The period of the function is so values will repeat every degrees in both directions.
, for any integer
, for any integer
, for any integer
Set equal to and solve for .
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Set equal to .
Solve for .
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Subtract from both sides of the equation.
Take the inversesine of both sides of the equation to extract from inside the sine.
Simplify the right side.
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The exact value of is .
The sinefunction is negative in the third and fourth quadrants. To find the secondsolution, subtract the solution from , to find a reference angle. Next, add this reference angle to to find the solution in the third quadrant.
Simplify the expression to find the secondsolution.
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Subtract from .
The resulting angle of is positive, less than , and coterminal with .
Find the period of .
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The period of the function can be calculated using .
Replace with in the formula for period.
The absolute value is the distance between a number and zero. The distance between and is .
Divide by .
Add to every negative angle to get positive angles.
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Add to to find the positive angle.
Subtract from .
List the new angles.
The period of the function is so values will repeat every degrees in both directions.
, for any integer
, for any integer
, for any integer
The final solution is all the values that make true.
, for any integer
Consolidate and to .
, for any integer
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