The function \( f \) is defined by \( y=a \cos k(x-b) \) or \( y=a \sin k(x-b) \), where \( k>0 \) and \( b \geq 0 \). The function \( g \) is defined by \( y=\tan c(x-d) \), where \( c>0 \) and \( d>0 \). Use the graphs of \( f \) and \( g \) to answer the following question. If we consider the graph of \( f \) as a cosine curve in the \( x \)-axis Which of the following will represent the equation of \( f \) ? Choose the correct option.

The equation of the cosine curve can be expressed in the general form \( y = a \cos(k(x - b)) \). In this form, \( a \) represents the amplitude, \( k \) controls the period of the function (calculated as \( \frac{2\pi}{k} \)), and \( b \) represents a horizontal shift or phase shift of the graph. When \( k \) is greater than zero, this cosine function will oscillate between \( -a \) and \( a \), creating the classic wave-like pattern associated with cosine curves. For the sine function given by \( y = a \sin(k(x - b)) \), it's similar but starts at the origin if \( b = 0 \). The critical aspect is that both functions will have different starting points due to the phase shift introduced by \( b \), but the amplitude \( a \) and frequency \( k \) remain essential components in determining the shape and spread of the wave. While the cosine function may begin at its maximum or minimum, sine functions typically begin at zero. To identify which specific equation corresponds to \( f \), one would look for the form that includes the parameters \( a \), \( k \), and \( b\).