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If x = sin^(-1)(1/3), then what is the value of cos(x)?

Practice Questions

Q1
If x = sin^(-1)(1/3), then what is the value of cos(x)?
  1. √(8)/3
  2. √(2)/3
  3. 1/3
  4. 2/3

Questions & Step-by-Step Solutions

If x = sin^(-1)(1/3), then what is the value of cos(x)?
  • Step 1: Understand that x = sin^(-1)(1/3) means that sin(x) = 1/3.
  • Step 2: Use the identity cos(x) = √(1 - sin^2(x)).
  • Step 3: Calculate sin^2(x). Since sin(x) = 1/3, we have sin^2(x) = (1/3)^2 = 1/9.
  • Step 4: Substitute sin^2(x) into the identity: cos(x) = √(1 - 1/9).
  • Step 5: Simplify the expression inside the square root: 1 - 1/9 = 9/9 - 1/9 = 8/9.
  • Step 6: Now, we have cos(x) = √(8/9).
  • Step 7: Simplify √(8/9) to √8 / √9 = √8 / 3.
  • Step 8: The final answer is cos(x) = √8 / 3.
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