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

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

Options:

  1. nπ/2
  2. nπ + π/2
  3. nπ + π

Correct Answer:

Solution:

sin(x) = 0 at x = nπ, where n is any integer.

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

Practice Questions

Q1
If sin(x) = 0, what are the possible values of x?
  1. nπ/2
  2. nπ + π/2
  3. nπ + π

Questions & Step-by-Step Solutions

If sin(x) = 0, what are the possible values of x?
Correct Answer: x = nπ, where n is any integer
  • Step 1: Understand that sin(x) is a function that gives the sine of an angle x.
  • Step 2: Know that sin(x) equals 0 at specific angles.
  • Step 3: Recall that the sine function is 0 at angles like 0, π, 2π, -π, -2π, etc.
  • Step 4: Recognize that these angles can be expressed in a general form as nπ, where n is any integer (like 0, 1, -1, 2, -2, etc.).
  • Step 5: Conclude that the possible values of x are all multiples of π.
  • Trigonometric Functions – Understanding the properties and values of the sine function, particularly where it equals zero.
  • Periodic Functions – Recognizing that sine is a periodic function with a period of 2π, leading to multiple solutions.
  • Integer Multiples – Identifying that the solutions involve integer multiples of π.
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