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Which formula gives the zeros of [tex]$y = \sin(x)$[/tex]?

A. [tex]kx[/tex] for any positive integer [tex]k[/tex]
B. [tex]kx[/tex] for any integer [tex]k[/tex]
C. [tex]\frac{k \pi}{2}[/tex] for any positive integer [tex]k[/tex]
D. [tex]\frac{k \pi}{2}[/tex] for any integer [tex]k[/tex]

Sagot :

GinnyAnswer
To find the zeros of the function [tex]\( y = \sin(x) \)[/tex], we need to determine where the sine function equals zero, i.e., where [tex]\( \sin(x) = 0 \)[/tex].

The sine function is known to have zeros at specific points on the x-axis. These points are the values where the function intersects the x-axis. The sine function [tex]\( \sin(x) \)[/tex] equals zero whenever [tex]\( x \)[/tex] is a multiple of [tex]\( \pi \)[/tex]. This is because the sine of any integer multiple of [tex]\( \pi \)[/tex] is zero. Mathematically, this can be expressed as:
[tex]\[ x = k \pi \][/tex]
where [tex]\( k \)[/tex] is an integer (not just positive integers, but any integer – positive, negative, or zero).

Thus, the zeros of [tex]\( y = \sin(x) \)[/tex] occur at:
[tex]\[ x = k \pi \][/tex]
for any integer [tex]\( k \)[/tex].

Among the given options, the correct formula that represents these zeros is:
[tex]\[ k \pi \text{ for any integer } k \][/tex]

Therefore, the correct answer is not among the provided options. If there had been an accurate representation, it would have been:
[tex]\[ k \pi \text{ for any integer } k \][/tex]
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