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

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

Options:

  1. 1
  2. 0
  3. -1
  4. undefined

Correct Answer: 1

Solution: 

If sin(x) = 0, then cos(x) can be either 1 or -1 depending on the angle x.

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

Practice Questions

Q1
If sin(x) = 0, what is the value of cos(x)?
  1. 1
  2. 0
  3. -1
  4. undefined

Questions & Step-by-Step Solutions

If sin(x) = 0, what is the value of cos(x)?
Correct Answer: 1 or -1
  • Step 1: Understand that sin(x) = 0 means that the sine of angle x is zero.
  • Step 2: Recall that sine is zero at specific angles: 0 degrees, 180 degrees, 360 degrees, etc. (or in radians: 0, Ï€, 2Ï€, ...).
  • Step 3: For these angles, find the corresponding cosine values.
  • Step 4: Calculate cos(0) which equals 1.
  • Step 5: Calculate cos(Ï€) which equals -1.
  • Step 6: Conclude that if sin(x) = 0, then cos(x) can be either 1 or -1 depending on the angle x.
  • Trigonometric Functions – Understanding the relationship between sine and cosine functions, particularly their values at specific angles.
  • Unit Circle – Using the unit circle to determine the values of sine and cosine at key angles.
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