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If cos(x) = 0, what is the value of x?

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Question: If cos(x) = 0, what is the value of x?

Options:

  1. π/2 + nπ
  2. nπ
  3. 0
  4. π

Correct Answer: π/2 + nπ

Solution: 

cos(x) = 0 at x = π/2 + nπ, where n is any integer.

If cos(x) = 0, what is the value of x?

Practice Questions

Q1
If cos(x) = 0, what is the value of x?
  1. π/2 + nπ
  2. nπ
  3. 0
  4. π

Questions & Step-by-Step Solutions

If cos(x) = 0, what is the value of x?
Correct Answer: π/2 + nπ
  • Step 1: Understand that cos(x) is a trigonometric function that gives the cosine of an angle x.
  • Step 2: Know that cos(x) = 0 at specific angles on the unit circle.
  • Step 3: Identify the angles where the cosine value is zero. These angles are π/2 (90 degrees) and 3π/2 (270 degrees).
  • Step 4: Recognize that these angles repeat every full rotation (2π radians).
  • Step 5: Write the general formula for these angles: x = π/2 + nπ, where n is any integer (0, ±1, ±2, ...).
  • Step 6: Conclude that the value of x can be any angle of the form π/2 + nπ.
  • Trigonometric Functions – Understanding the behavior of the cosine function and its values at specific angles.
  • Periodic Functions – Recognizing that cosine is a periodic function with a period of 2π.
  • General Solutions – Finding general solutions for trigonometric equations involving integer multiples.
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