Solve 2sin(2x-π/2) +1 Equation for Sine Curve

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In summary, the 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 can be represented by the equation 2sin(2x-π/2)+1. To find the phase shift, you can use the formula c/b, where c represents the horizontal shift and b represents the coefficient of x. In this case, c = π/2 and b = 2, so the phase shift is π/4. This means that the curve is shifted to the right by π/4 units on the x-axis. You can verify this by plugging in x = π/2 into the equation and seeing the resulting value.
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krutika
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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!
 
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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!

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
 
  • #3
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

okay but i still don't understand how to find it? like i know the formula is c/b? but i don't get how to find the number?
 

FAQ: Solve 2sin(2x-π/2) +1 Equation for Sine Curve

What is the equation for a sine curve?

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.

How do you solve an equation for a sine curve?

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.

How do you solve 2sin(2x-π/2) +1 Equation for Sine Curve?

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.

What is the period of a sine curve?

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.

How do you graph a sine curve?

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.

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