how do you solve for y=sinX+2. just the phase shift and period. even how to graph if anyone knows. i got stuck with this one

To find the phase shift and period of the function y = sin(x) + 2, you need to understand the properties of the sine function.

1. Phase Shift:
The general form of the sine function is y = a*sin(b(x - h)) + k, where (h, k) represents the phase shift - specifically, (h, k) is the point on the graph where the function starts repeating.

In this case, y = sin(x) + 2, the phase shift (h) is 0. This means there is no shift in the graph along the x-axis; it starts at the usual point (0, 2).

2. Period:
The period (T) represents the horizontal length of one complete cycle of the function. For the standard sine function, y = sin(x), the period is 2π radians.

In this case, y = sin(x) + 2, adding 2 to sin(x) does not affect the period. Therefore, the period remains 2π radians.

To graph the function y = sin(x) + 2:
1. Choose a range for x-axis, such as -2π to 2π.
2. Divide the range into intervals of length π/4, π/2, or any suitable length for the x-axis.
3. Calculate corresponding y-values by substituting x-values into the function.
4. Plot the points (x, y) on the graph.
5. Connect the points with a smooth curve.

Keep in mind that adding a constant value of 2 to the sine function will shift the graph vertically upward by 2 units.