Which of the following functions is not a sinusoid?
A. $y=\sin x$
B. $y=\sqrt{x}$
C. $y=\cos x$
D. None of the above are sinusoids.
Answer (1)
Sinusoids are functions of the form A \[ s in ] ( B x + C ) + D or A \[ cos ] ( B x + C ) + D .
y = \[ s in ] x and y = cos x are sinusoids.
y = x is not a sinusoid.
The function that is not a sinusoid is y = x .
Explanation
Understanding Sinusoids We need to determine which of the given functions is not a sinusoid. A sinusoid is a function that can be written in the form A \[ s in ] ( B x + C ) + D or A \[ cos ] ( B x + C ) + D , where A, B, C, and D are constants.
Analyzing the Options Let's examine each option:
A. y = \[ s in ] x . This is a sinusoid with A = 1 , B = 1 , C = 0 , and D = 0 . So, it is a sinusoid.
B. y = x . This is a square root function, which is not a sinusoid. It does not oscillate like sine or cosine functions.
C. y = cos x . This is a sinusoid with A = 1 , B = 1 , C = 0 , and D = 0 . So, it is a sinusoid.
Identifying the Non-Sinusoid Therefore, the function that is not a sinusoid is y = x .
Examples
Sinusoids are used to model many real-world phenomena, such as sound waves, light waves, and alternating current. Understanding sinusoids helps in analyzing these phenomena. The square root function, on the other hand, appears in various contexts such as calculating distances or growth rates, but it doesn't share the oscillatory nature of sinusoids.
