Trigonometric Identities and Equations: Background You’ll Need 4

  • Identify the period, amplitude and midline of a sinusoidal function

A sinusoidal function is a sine or cosine graph of the form:

[latex]y = A\sin(Bx) + D \quad \text{or} \quad y = A\cos(Bx) + D[/latex]

  • Amplitude [latex]|A|[/latex]: height from the midline to a peak or trough

  • Period: [latex]\frac{2\pi}{B}[/latex]: horizontal length of one full cycle

  • Midline: [latex]y = D[/latex]: vertical center line of the wave

Find the amplitude, period, and midline of
[latex]y = 3\sin(2x) - 1[/latex].