Complementary function to sin(x)
cos(x)
The complementary function to sin(x) is the function that, when added to sin(x), will produce a constant value. In other words, if y(x) is the complementary function to sin(x), then y(x) + sin(x) = C, where C is a constant.
To find the complementary function to sin(x), one can consider the fact that the sine function has a period of 2π and oscillates between -1 and 1. Therefore, a possible complementary function would be a constant value that cancels out or balances the oscillations of sin(x) and results in a constant function.
One such complementary function is -sin(x). If we add sin(x) and -sin(x), we get sin(x) – sin(x) = 0, which is a constant value. Therefore, -sin(x) can be considered as the complementary function to sin(x).
It is important to note that this is not the only possible complementary function to sin(x). Any constant multiple of -sin(x) would also serve as the complementary function. For example, -2sin(x), 0.5sin(x), or any other constant multiplied by -sin(x) would also satisfy the condition y(x) + sin(x) = C.
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