Determine the amplitude of: y=-2sinx
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A typical trigonometric function such as
f(x) = a sin k(x-φ)
has the following definitions:
amplitude = |a|, or the absolute value of a
period = 2π/k
phase shift = φ
For example,
y = 3 sin 2(x-π/4)
has an amplitude of 3, period of 2π/2=π, and phase shift of π/4 to the right.
So for y = -2 sin x,
the amplitude would be |-2| = 2.
To determine the amplitude of the function y = -2sin(x), you need to understand the properties of the sine function and how they affect the amplitude.
The general form of a sine function is y = A*sin(Bx), where A represents the amplitude and B controls the period of the function. In this case, the amplitude is given as -2.
The amplitude of a sine function determines the maximum value of the function's oscillation above and below the x-axis. It represents the height of the wave.
In this case, the amplitude is -2, which means the maximum positive value of the function is 2 and the maximum negative value is -2. The graph of the function will oscillate between these values as the x values vary.
To summarize, the amplitude of the function y = -2sin(x) is 2.