The amplitude of a sinusoidal function is half the difference between its maximum and minimum values. Amplitude = $$\frac{\text{Maximum Value} - \text{Minimum Value}}{2}$$. For this function, the amplitude is $$\frac{10 - (-2)}{2} = \frac{12}{2} = 6$$.

To find the phase shift, we must factor the coefficient of $$x$$ from the argument of the sine function. $$4x+\pi = 4(x+\frac{\pi}{4})$$. The function becomes $$f(x) = -2\sin(4(x+\frac{\pi}{4}))+1$$. This is of the form $$y = a\sin(b(x-c))+d$$ where $$c = -\frac{\pi}{4}$$. This represents a phase shift of $$\frac{\pi}{4}$$ units to the left.

For $$f(x)=-3\sin(\frac{1}{2}x + \frac{\pi}{2}) - 1$$: The amplitude is $$|-3|=3$$. The midline is $$y=-1$$. The period is $$\frac{2\pi}{1/2}=4\pi$$. The phase shift requires factoring: $$\frac{1}{2}(x+\pi)$$, so the shift is $$\pi$$ units to the left. The maximum value is $$-1+3=2$$ and the minimum is $$-1-3=-4$$. Therefore, the statement that the amplitude is 3 and the midline is $$y=-1$$ is correct.

For a sinusoidal function $$y = a\sin(b(x-c))+d$$: The amplitude $$|a|=4$$. The midline $$y=d$$ is $$y=-1$$. The phase shift $$c$$ is $$\frac{\pi}{2}$$ to the right. The period is $$\frac{2\pi}{|b|} = \pi$$, which implies $$|b|=2$$. Combining these parameters gives the equation $$y = 4\sin(2(x - \frac{\pi}{2})) - 1$$.

The period of a sinusoidal function of the form $$y = a\cos(b(x-c))+d$$ is given by the formula $$P = \frac{2\pi}{|b|}$$. In the function $$g(x) = -4\cos(\frac{\pi}{3}x + \pi) - 2$$, the value of $$b$$ is $$\frac{\pi}{3}$$. Therefore, the period is $$P = \frac{2\pi}{\pi/3} = 2\pi \cdot \frac{3}{\pi} = 6$$.

The amplitude of a sinusoidal function of the form $$f(t) = d + a\sin(b(t-c))$$ is the absolute value of $$a$$. In the function $$f(t) = 5 - 3\sin(4t + 1)$$, the value of $$a$$ is $$-3$$. The amplitude is $$|-3| = 3$$.

The midline of a sinusoidal function of the form $$h(x) = a\sin(b(x-c))+d$$ is the horizontal line $$y = d$$. For the function $$h(x) = 2\sin(\pi(x-1)) + 7$$, the value of $$d$$ is 7. Thus, the equation of the midline is $$y = 7$$.

The period of the function $$g(x) = A\cos(Bx+C)+D$$ is given by $$P = \frac{2\pi}{|B|}$$. Therefore, changing the value of $$B$$ alters the period by causing a horizontal stretch or compression.

The maximum value of a sinusoidal function is the midline plus the amplitude, and the minimum value is the midline minus the amplitude. Maximum Value = $$d + |a| = 2 + 5 = 7$$. Minimum Value = $$d - |a| = 2 - 5 = -3$$.

The graph of $$y=\cos(x)$$ shifted to the right by $$\frac{\pi}{2}$$ units results in the graph of $$y=\sin(x)$$. This is a known trigonometric identity: $$\sin(x) = \cos(x - \frac{\pi}{2})$$.