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If cot(x) = 5/12, what is sin(x)?

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Question: If cot(x) = 5/12, what is sin(x)?

Options:

  1. 12/13
  2. 5/13
  3. 13/12
  4. 5/12

Correct Answer: 12/13

Solution: 

Using the identity cot(x) = cos(x)/sin(x), we can find sin(x) = 12/13 using the Pythagorean theorem.

If cot(x) = 5/12, what is sin(x)?

Practice Questions

Q1
If cot(x) = 5/12, what is sin(x)?
  1. 12/13
  2. 5/13
  3. 13/12
  4. 5/12

Questions & Step-by-Step Solutions

If cot(x) = 5/12, what is sin(x)?
  • Step 1: Understand that cot(x) is the ratio of cos(x) to sin(x). So, cot(x) = cos(x) / sin(x).
  • Step 2: Given cot(x) = 5/12, we can write this as cos(x) / sin(x) = 5/12.
  • Step 3: Let sin(x) = 12k and cos(x) = 5k for some value k. This keeps the ratio the same.
  • Step 4: Use the Pythagorean theorem, which states that sin^2(x) + cos^2(x) = 1.
  • Step 5: Substitute sin(x) and cos(x) into the equation: (12k)^2 + (5k)^2 = 1.
  • Step 6: Simplify the equation: 144k^2 + 25k^2 = 1, which gives 169k^2 = 1.
  • Step 7: Solve for k: k^2 = 1/169, so k = 1/13.
  • Step 8: Now find sin(x): sin(x) = 12k = 12 * (1/13) = 12/13.
  • Trigonometric Identities – Understanding the relationship between cotangent, sine, and cosine using the identity cot(x) = cos(x)/sin(x).
  • Pythagorean Theorem in Trigonometry – Applying the Pythagorean theorem to find the lengths of the sides of a right triangle when given one of the trigonometric ratios.
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