Final answer:
In the equation y = a sin(bx + c), 'c' affects the phase shift by shifting the graph horizontally (x-value), while 'b' changes the frequency, influencing the period of the wave pattern (x-value).
Step-by-step explanation:
The coefficients 'c' and 'b' in the trigonometric function y = a sin(bx + c) affect the phase shift and the periodicity of the graph, respectively. The value 'c' represents the phase shift and directly impacts the x-value by shifting the graph horizontally. If 'c' is positive, the graph shifts to the left; if negative, to the right. This means, 'c' involves a shift along the x-axis without affecting the y-values. On the other hand, the coefficient 'b' affects the frequency of the function, which influences the x-value in the sense that it alters the period or the distance between successive repetitions of the wave pattern. A higher value of 'b' results in more cycles within a given x-range (decreases the period), whereas a lower value means fewer cycles (increases the period). Therefore, 'c' affects the phase shift (x-value) and 'b' affects the periodicity (also indirectly an aspect of the x-value).