Determine the amplitude and period of the function without graphing.
y = 7/3sin (-2π/3x)
To determine the amplitude and period of the function y = (7/3)sin(-(2π/3)x) without graphing, we can use the equations for the general form of a sinusoidal function:
y = A*sin(Bx + C) + D
In this case, A is the amplitude, B affects the period, and C is an optional phase shift.
Comparing the given function y = (7/3)sin(-(2π/3)x) to the general form, we can see that A = 7/3. Therefore, the amplitude is |7/3| = 7/3.
For the period, we need to find B in the equation Bx. In the given function, B = -(2π/3). The period is given by the formula:
Period = 2π/|B|
Substituting -(2π/3) for B, we can calculate the period:
Period = 2π/|-(2π/3)| = 2π/(2π/3) = 3
Therefore, the period of the function is 3.