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# Trigonometry Examples

Interchange the variables.

Rewrite the equation as .

Combine and .

Multiply each term by and simplify.

Multiply each term in by .

Simplify the left side of the equation by cancelling the common factors.

Dividing two negative values results in a positive value.

Multiply the numerator by the reciprocal of the denominator.

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Move to the left of .

Take the inverse sine of both sides of the equation to extract from inside the sine.

Multiply both sides of the equation by .

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Multiply both sides of the equation by .

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Replace the with to show the final answer.

Set up the composite result function.

Evaluate by substituting in the value of into .

Combine and .

Cancel the common factor of .

Move the leading negative in into the numerator.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Multiply.

Multiply by .

Multiply by .

Since , is the inverse of .