Answer
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Step 1:I'll solve this step by step following the specified LaTeX formatting guidelines:
Step 2:: Understand the Trigonometric Equation
The equation $$\cos(x) = 1$$ means we are looking for all angle values where the cosine function equals 1.
Step 3:: Recall the Unit Circle Properties
In the unit circle, $$\cos(x)$$ equals 1 only at specific angle values.
These are points where the cosine function reaches its maximum value of 1.
Step 4:: Identify the Angle Solutions
- And so on for all integer values of $$k
The cosine function equals 1 at the following angles: This means the solutions are:
Final Answer
The solutions are x = 2\pi k, where k \in \mathbb{Z} (k is any integer), which includes ..., - 4\pi, - 2\pi, 0, 2\pi, 4\pi, ...
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