Q:

# How do you factor sin(3x)?

A:

The expression sin(3x) cannot be factored. Factoring is the process of finding what to multiply together to get an expression. Rather than being an expression, sine is a trigonometric function of an angle of a right-angled triangle that represents the ratio of the length of the opposite side to the length of the hypotenuse, the longest side of the angle. To solve y = sin(3x), make an equation for the integer. Then you can solve the equation for the variable x, and interpret the results.

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1. Form an equation with an integer

The zeros of y = sin(x) are multiples of pi (π). Therefore: 3x = nπ, where n represents an integer. This represents a multiple of pi.

2. Solve the equation

Solve the equation for x by dividing nπ by three so the equation reads: x = (nπ)/3).

3. Interpret the results

The equation x = (nπ)/3 means that the function equals zero at all multiples of π/3, such as π/3, (2π)/3, π, (4π)/3 and so on in both positive and negative directions.

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