Which of the following is the standard form of a sine graph?

The standard form of a sine graph is expressed as A * sin(Bt + C). In this form, "A" represents the amplitude of the sine wave, which determines the height of the wave's peaks and the depth of its troughs. The "B" value affects the period of the sine function, indicating how frequently the wave oscillates within a given interval. Specifically, the period can be calculated as (2π/B). The "C" value is the phase shift, which determines the horizontal translation of the graph along the t-axis.

The form is well-used because it allows for easy manipulation and understanding of transformations applied to the basic sine curve, familiar to students. Thus, the use of sine in the correct answer aligns perfectly with the characteristics of periodic functions that oscillate smoothly between their maximum and minimum values.

Other options, such as cosine, cotangent, and tangent forms, represent different types of periodic functions. While they also exhibit oscillatory behavior, their representations and properties do not reflect the standard sine graph characteristics.