# Solve for x -sin(pix)=1

Multiply each term in by
Multiply each term in by .
Multiply .
Multiply by .
Multiply by .
Multiply by .
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.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Simplify .
Cancel the common factor of .
Move the leading negative in into the numerator.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Move the negative in front of the fraction.
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.
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 .
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 .
Combine.
Multiply by .
Combine the numerators over the common denominator.
Multiply by .
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Cancel the common factor of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Find the period.
The period of the function can be calculated using .
Replace with in the formula for period.
Solve the equation.
is approximately which is positive so remove the absolute value
Cancel the common factor of .
Cancel the common factor.
Divide by .
Add to every negative angle to get positive angles.
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 .
Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply by .
Subtract from .
List the new angles.
The period of the function is so values will repeat every radians in both directions.
, for any integer