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

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

Options:

  1. 0
  2. 1
  3. undefined
  4. ∞

Correct Answer: undefined

Solution: 

tan(x) = sin(x)/cos(x). If sin(x) = 0, then tan(x) is undefined when cos(x) = 0.

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

Practice Questions

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

Questions & Step-by-Step Solutions

If sin(x) = 0, what is the value of tan(x)?
  • Step 1: Understand that sin(x) = 0 means that the sine of angle x is zero.
  • Step 2: Recall the definition of tangent: tan(x) = sin(x) / cos(x).
  • Step 3: Since sin(x) = 0, we can substitute this into the tangent formula: tan(x) = 0 / cos(x).
  • Step 4: When you divide 0 by any number (as long as that number is not zero), the result is 0. So, tan(x) = 0 / cos(x) = 0 if cos(x) is not zero.
  • Step 5: However, if cos(x) = 0, then we cannot divide by zero, and tan(x) is undefined.
  • Step 6: Therefore, tan(x) is 0 when cos(x) is not zero, and undefined when cos(x) = 0.
  • Trigonometric Functions – Understanding the relationships between sine, cosine, and tangent functions.
  • Undefined Values – Recognizing when a trigonometric function is undefined due to division by zero.
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