The amplitude of a sine wave is the distance from the midline to the highest or lowest point on the curve. It represents the maximum displacement of the wave from its equilibrium position.
The period of a sine wave is the length of one complete cycle of the wave. It can be calculated by dividing 2π by the frequency of the wave, or by dividing the circumference of the unit circle by the x-coordinate of a point on the wave.
The phase shift of a sine wave is the horizontal displacement of the wave from its original position. It is usually measured in radians or degrees and can be positive or negative depending on the direction of the shift.
The vertical shift of a sine wave is the vertical displacement of the wave from its equilibrium position. It is usually measured in units or degrees and can be positive or negative depending on the direction of the shift. The vertical shift does not affect the shape or period of the wave, but only its position on the y-axis.
To solve a sin equation, you can use the general form of the equation: y = A*sin(Bx+C) + D, where A is the amplitude, B is the frequency (1/period), C is the phase shift, and D is the vertical shift. Plug in the given values and solve for x to find the solutions to the equation.