krutika said:A sine curve with a period of π , an amplitude of 2, a right phase shift of π/2, and a vertical translation up 1 unit
what i have so far is 2sin(2x- ____ ) +1... i just don't know how to solve the phase shift part...please help and give me the steps. thanks!
SuperSonic4 said:The phase shift is the horizontal shift on the x-axis and is equal to \(\displaystyle \frac{\pi}{2}\). A movement to the right is minus and to the left is plus.
The way I remember it is that it's opposite from a number line. You can verify this for yourself by checking f(pi/2) and seeing what you get
The equation for a sine curve is y = A*sin(Bx + C) + D, where A is the amplitude, B is the frequency, C is the phase shift, and D is the vertical shift.
To solve an equation for a sine curve, you need to isolate the sine function on one side of the equation and use inverse operations to solve for the variable.
To solve 2sin(2x-π/2) +1 for a sine curve, use inverse operations to isolate the sine function: 2sin(2x-π/2) = -1. Then, divide both sides by 2 to get sin(2x-π/2) = -1/2. Finally, use inverse sine to solve for x: 2x-π/2 = arcsin(-1/2). Simplify and solve for x to get the solution.
The period of a sine curve is the distance between two consecutive peaks (or troughs) of the curve. It is equal to 2π/B, where B is the frequency in the equation y = A*sin(Bx + C) + D.
To graph a sine curve, plot several points using the equation y = A*sin(Bx + C) + D. These points will form a smooth curve. Be sure to label the amplitude, frequency, phase shift, and vertical shift on the graph. You can also use a graphing calculator or software to graph the curve.