Question

Decide whether or not the following are statements. In the case of a statement, say if it is true or false, if possible. \(\cos (x)=-1\)

Short answer

The given expression \(\cos(x) = -1\) is a mathematical statement. This is true if \(x\) corresponds to multiples of \(\pi\) plus \(\pi\), and false for other values of \(x\).

Step-by-step solution

Recognize Mathematical Statement

Identify the statement and understand that we need to check if \(\cos(x) = -1\) is true or false. This is a mathematical statement that can be resolved.

Evaluate Statement

The cosine function oscillates between -1 and 1. The function \(\cos(x)\) equals -1 only when \(x\) corresponds to multiples of \(\pi\) plus \(\pi\), this can be expressed as \(x = n\pi + \(\pi\) \), where \(n\) is an integer. For other values of \(x\), the statement is false.