Let's analyze the given function:
y = 5sin(3x - 180°) - 2
Amplitude: The coefficient of the sine function, 5, represents the amplitude of the sinusoidal wave. Therefore, the amplitude of the function is 5.
Period: The period of the sine function is determined by the coefficient of x inside the parentheses, which is 3 in this case. The formula for the period, T, of a sine function is T = 2π/|b|, where b is the coefficient of x. So, in our case, the period is T = 2π/3.
Phase Shift: The phase shift of the sine function is determined by the constant term inside the parentheses, which is -180° in this case. To find the phase shift, we need to solve the equation 3x - 180° = 0. Solving for x, we get x = 60°. Therefore, the phase shift is 60° to the right.
Equation of Axis: The equation of the axis represents the horizontal line that the sinusoidal wave oscillates around. In this case, the equation of the axis can be determined by taking the average of the maximum and minimum values of the function. Since the amplitude is -2, the equation of the axis is y = -2.
Maximum and Minimum Values: The maximum and minimum values of the function can be found by adding and subtracting the amplitude from the equation of the axis. In this case, the maximum value is -2 + 5 = 3, and the minimum value is -2 - 5 = -7.
To summarize:
- Amplitude: 5
- Period: 2π/3
- Phase Shift: 60° to the right
- Equation of Axis: y = -2
- Maximum Value: 3
- Minimum Value: -7