Solve for x -sin(pix)=1

Math
Multiply each term in by
Tap for more steps…
Multiply each term in by .
Multiply .
Tap for more steps…
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.
Tap for more steps…
Divide each term in by .
Cancel the common factor of .
Tap for more steps…
Cancel the common factor.
Divide by .
Simplify .
Tap for more steps…
Cancel the common factor of .
Tap for more steps…
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.
Tap for more steps…
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 .
Tap for more steps…
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 .
Tap for more steps…
Combine.
Multiply by .
Combine the numerators over the common denominator.
Add and .
Multiply by .
Add and .
Divide each term by and simplify.
Tap for more steps…
Divide each term in by .
Cancel the common factor of .
Tap for more steps…
Cancel the common factor.
Divide by .
Cancel the common factor of .
Tap for more steps…
Factor out of .
Cancel the common factor.
Rewrite the expression.
Find the period.
Tap for more steps…
The period of the function can be calculated using .
Replace with in the formula for period.
Solve the equation.
Tap for more steps…
is approximately which is positive so remove the absolute value
Cancel the common factor of .
Tap for more steps…
Cancel the common factor.
Divide by .
Add to every negative angle to get positive angles.
Tap for more steps…
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 .
Tap for more steps…
Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
Tap for more steps…
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
Consolidate the answers.
, for any integer
Solve for x -sin(pix)=1

Download our
App from the store

Create a High Performed UI/UX Design from a Silicon Valley.

Scroll to top