The question about the equation -57 = cos(5x) has a problem since the cosine function cannot equal -57. The range for cosine is between -1 and 1, indicating a typo or mistake in the question that needs clarification.
The student has asked the question about the equation of the graph represented by the expression -57 = cos(5x). Unfortunately, there seems to be a misunderstanding, because the cosine function ranges from -1 to 1, hence it cannot equal -57. It is likely that there is a typo or error in the question. For a typical cosine equation of the form y = cos(kx), where k is the frequency, the graph would be an oscillating wave along the x-axis between 1 and -1. If the equation were valid, it would represent a horizontal line which is not possible in the case of a cosine function. Therefore, we need to clarify the equation. If it was supposed to be the cosine of a different value or if there should've been another operation involved that was missed out.
The equation of the graph represented by the expression -57 = cos(5x) is cos(5x) = -57.
To solve the equation, we need to isolate x. We can do this by taking the inverse cosine function (also known as arccos) of both sides:
arccos(cos(5x)) = arccos(-57)
The right side of the equation is not valid because the range of the inverse cosine function is limited to -1 to 1, so there is no solution to the equation.
The question probably may be:
What is the equation of the graph represented by the expression -57 = cos(5x)?