Find the magnitude of the trig term by taking the absolute value of the coefficient.

The lower bound of the range for sine is found by substituting the negative magnitude of the coefficient into the equation.

Simplify .

To write as a fraction with a common denominator, multiply by .

Combine and .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by .

Add and .

Move the negative in front of the fraction.

The upper bound of the range for sine is found by substituting the positive magnitude of the coefficient into the equation.

Simplify .

Write as a fraction with a common denominator.

Combine the numerators over the common denominator.

Add and .

The range is .

Interval Notation:

Set-Builder Notation:

Find the Range y=4/5sin(x)