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If cos(x) = 0, what are the possible values of x?

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Question: If cos(x) = 0, what are the possible values of x?

Options:

  1. 90° + k*180°
  2. k*90°
  3. k*180°
  4. 0° + k*360°

Correct Answer: 90° + k*180°

Solution: 

cos(x) = 0 at x = 90° + k*180°, where k is any integer.

If cos(x) = 0, what are the possible values of x?

Practice Questions

Q1
If cos(x) = 0, what are the possible values of x?
  1. 90° + k*180°
  2. k*90°
  3. k*180°
  4. 0° + k*360°

Questions & Step-by-Step Solutions

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, ...).
  • Trigonometric Functions – Understanding the behavior of the cosine function and its periodicity.
  • General Solutions – Finding all possible angles that satisfy the equation using the general solution format.
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