Solve for ? sin(3x)=-1

Solve for ? sin(3x)=-1
Take the inverse sine of both sides of the equation to extract from inside the sine.
The exact value of is .
Divide each term by and simplify.
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Divide each term in by .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Multiply .
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Multiply and .
Multiply by .
The sine function is negative in the third and fourth quadrants. To find the second solution, 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 second solution.
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To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Combine.
Multiply by .
Combine the numerators over the common denominator.
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Combine.
Multiply by .
Combine the numerators over the common denominator.
Add and .
Multiply by .
Add and .
Divide each term by and simplify.
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Divide each term in by .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Multiply .
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Multiply and .
Multiply by .
Find the period.
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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 .
Add to every negative angle to get positive angles.
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Add to to find the positive angle.
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
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Multiply by .
Subtract from .
Cancel the common factor of and .
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Factor out of .
Cancel the common factors.
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Factor out of .
Cancel the common factor.
Rewrite the expression.
List the new angles.
The period of the function is so values will repeat every radians in both directions.
, for any integer
Consolidate the answers.
, for any integer
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