How Do You Factor Sin(3x)?


Quick Answer

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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Full Answer

  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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