In the equation y=sin x +10, what is the amplitude, period, vertical shift, and phase shift?
Use the form a sin (bx−c) +d
to find the amplitude, period, phase shift, and vertical shift.
Amplitude: 1
Period: 2π
Phase Shift: None
Vertical Shift: 10
Hope I helped friend!
To find the amplitude, period, vertical shift, and phase shift of the equation y = sin(x) + 10, we can analyze the general form of a sinusoidal function: y = A * sin(Bx + C) + D.
Amplitude (A): The amplitude represents the vertical distance between the maximum and minimum values of the function. In this case, the amplitude is simply 1 since sin(x) has an amplitude of 1.
Period (P): The period represents the horizontal distance between two consecutive points on the graph with the same value (usually the maximum or minimum points). For a basic sin(x) function, the period is equal to 2π. However, in this equation, the value of B is not mentioned, so we need to determine that first.
To find B, we can compare our equation to the general form: sin(Bx + C). In our equation sin(x), we can recognize that B = 1, and since it is not mentioned, it is implicitly considered as 1.
Given that B = 1, the period (P) of our equation is 2π/B, which is 2π/1, resulting in a period of 2π.
Vertical shift (D): The vertical shift represents the vertical translation of the graph and is equal to the constant term D in the equation. In our equation sin(x) + 10, the vertical shift is upward by 10 units since D = 10.
Phase shift (C): The phase shift represents the horizontal translation of the graph and is calculated as C/B. In our equation sin(x) + 10, the phase shift is 0 since C = 0.
In summary:
- Amplitude (A) = 1
- Period (P) = 2π
- Vertical shift (D) = 10
- Phase shift (C) = 0