What is the maximum value of [tex]y[/tex] for [tex]y=2 \sin x[/tex]?
Answer (2)
The function is y = 2 sin x .
The maximum value of sin x is 1.
Multiply the maximum value of sin x by 2 to find the maximum value of y : 2 × 1 = 2 .
The maximum value of y is 2 .
Explanation
Problem Analysis We are given the function y = 2 sin x and we want to find the maximum value of y .
Maximum Value of Sine Function We know that the sine function, sin x , has a range of [ − 1 , 1 ] . This means that the maximum value of sin x is 1.
Calculating Maximum Value of y To find the maximum value of y , we multiply the maximum value of sin x by 2: y ma x = 2 × 1 = 2 .
Final Answer Therefore, the maximum value of y for the function y = 2 sin x is 2.
Examples
Imagine you're designing a simple electrical circuit where the voltage y varies sinusoidally with time x , described by the equation y = 2 sin x . Knowing that the maximum voltage is 2 volts helps you choose components that can safely handle this voltage without failing. This is a direct application of understanding the range and maximum values of trigonometric functions in a practical engineering context.
The maximum value of y for the function y = 2 sin x is 2, which is determined by the fact that the sine function reaches a maximum of 1. Therefore, multiplying this maximum by 2 gives us y = 2 . This understanding is essential in various disciplines that utilize sinusoidal functions.
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