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The amplitude of trigonometric functions is the maximum displacement on the graph of a function. In the case of the sine and cosine functions, this value is the leading coefficient of the function. If y = A sin x , then the amplitude is |A|.
Therefore, the amplitude of the function y = -5sin2x, is A = 5.
The period of trigonometric functions is the displacement of x at which the graph of a function begins to repeat. The general form of the sine function is as follows: f(x) = A sin Bx, where |A| is the amplitude and B determines the period. The period is found by the equation: P = 2π/B
P = 2π/2 = π
Therefore, the period of the function y = -5sin2x, is P = π.
The frequency of trigonometric functions are inversely related to the period of trigonometric functions. It is the number of cycles it completes in a given interval. If a general form of the sine function is f(x) = A sin Bx, then the frequency is B.
Therefore, the frequency of the function y = -5sin2x, is B = 2.
Answers:
- Amplitude = 5
- Period = π
- Frequency = 2