The domain would be the x variable, which is undefined so can be any real number.
The magnitude of the term is the absolute value of the coefficient. Since the equation does not contain a coefficient, the magnitude becomes 1.
The lower bound of the range is the negative magnitude which would be -1 and the upper bound is the magnitude, which is 1.
So the range is equal to -1 ≤ y ≤ 1
We can prove that y ranges between -1 and 1 by looking at cosx in triangle.
The extreme values that a function can take in its domain is known as its range for example the range of x for all real number is [-∞,∞].
The range of y = cosx is -1≤y≤1 because if we look at the definition of cosine in a triangle we find that cosine is = opposite/hypotenuse which means the opposite side is divided by the hypotenuse and we also know that the hypotenuse in a right-angled triangle is always greater than any of its other two sides, hence the ratio of a side to the hypotenuse will always be less than 1, but if the triangle is almost non-existent than at that stage the value of cosine is equal to 1. For the negative part, we can consider the angle to be in the negative plane and will get the value to be negative.
Hence, y=cos(x) ranges between -1 and 1 which implies -1≤y≤1, because of the interpretation of cosx.
Learn more about the range of cosine here
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