Describe the changes in the graph of the following funciton
h(t) = sin(4/3 - 2t)
To describe the changes in the graph of the function h(t) = sin(4/3 - 2t), we can consider the effects of the various components of the function.
1. Amplitude: The amplitude of a sine function determines the maximum distance the graph reaches from the midline. In this case, the function has a constant amplitude of 1. This means that the graph will oscillate between -1 and 1.
2. Phase Shift: The term 4/3 in the function represents a phase shift. A phase shift determines how the graph is shifted horizontally. In this case, since the equation is sin(4/3 - 2t), the graph is shifted to the right by 4/6 (or 2/3) units. This means that the graph will start at t = 0 when t = 4/6, and the pattern will be repeated every pi/1 units.
3. Frequency: The coefficient of t, which is -2 in this case, determines the frequency of the graph. The frequency represents the number of complete cycles the graph goes through in a specific interval. In this case, the function has a frequency of 2. This means that the graph will complete 2 full cycles within the range of the given values of t.
Therefore, the graph of h(t) = sin(4/3 - 2t) will oscillate between -1 and 1, start at t = 4/6 (or 2/3), and complete 2 cycles within the given range of t. Keep in mind that the graph may be reflected or inverted depending on the signs (+/-) present in the equation.