If cos(x) = 0, what are the possible values of x?
Correct Answer: x = 90° + k*180°
- Step 1: Understand that cos(x) represents the cosine of an angle x.
- Step 2: Recall that the cosine function equals 0 at specific angles.
- Step 3: Identify the first angle where cos(x) = 0, which is 90°.
- Step 4: Recognize that the cosine function is periodic, meaning it repeats its values.
- Step 5: Determine the period of the cosine function, which is 360°.
- Step 6: Since cos(x) = 0 at 90°, the next occurrence is 90° + 180° = 270°.
- Step 7: Generalize the solution by adding multiples of the period (180°) to 90°.
- Step 8: Write the general formula: x = 90° + k*180°, where k is any integer (0, ±1, ±2, ...).
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