Question

Rewrite the following function in terms of step functions. For step functions, remember to use sgn rather than sgn.

f(x) = 10sinx 3cosx
a) f(x) = 15sgn(sin(x))
b) f(x) = 30sgn(sin(x))
c) f(x) = 30sgn(cos(x))
d) f(x) = 15sgn(cos(x))

Answer 1

The task of rewriting f(x) = 10sin(x) + 3cos(x) in terms of step functions is not feasible without additional context or instruction, as the 'sgn' function based on sin(x) or cos(x) only yields -1, 0, or 1, which cannot account for the original coefficients.

The question pertains to expressing a trigonometric function in terms of step functions, specifically using the 'sgn' function, which represents the signum or sign function. The student seeks to rewrite f(x) = 10sin(x) + 3cos(x) using step functions. The correct step function representation is contingent upon the behavior of the trigonometric functions over the defined domains. Since, for any real number x, the signum of sin(x) and cos(x) will only return values of -1, 0, or 1, we cannot straightforwardly convert the original function into a form that uses the sgn function due to the coefficients 10 and 3 in front of the sine and cosine functions, respectively.