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If x = sin^(-1)(3/5), what is the value of cos(x)?

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Question: If x = sin^(-1)(3/5), what is the value of cos(x)?

Options:

  1. 4/5
  2. 3/5
  3. 2/5
  4. 1/5

Correct Answer: 4/5

Solution: 

Using the identity cos(x) = sqrt(1 - sin^2(x)), we have cos(x) = sqrt(1 - (3/5)^2) = sqrt(16/25) = 4/5.

If x = sin^(-1)(3/5), what is the value of cos(x)?

Practice Questions

Q1
If x = sin^(-1)(3/5), what is the value of cos(x)?
  1. 4/5
  2. 3/5
  3. 2/5
  4. 1/5

Questions & Step-by-Step Solutions

If x = sin^(-1)(3/5), what is the value of cos(x)?
Correct Answer: 4/5
  • Step 1: Understand that x = sin^(-1)(3/5) means that sin(x) = 3/5.
  • Step 2: Use the identity cos(x) = sqrt(1 - sin^2(x)).
  • Step 3: Calculate sin^2(x) which is (3/5)^2 = 9/25.
  • Step 4: Substitute sin^2(x) into the identity: cos(x) = sqrt(1 - 9/25).
  • Step 5: Simplify 1 - 9/25. Convert 1 to a fraction: 1 = 25/25, so 25/25 - 9/25 = 16/25.
  • Step 6: Now, cos(x) = sqrt(16/25).
  • Step 7: Calculate the square root: sqrt(16/25) = sqrt(16) / sqrt(25) = 4/5.
  • Inverse Trigonometric Functions – Understanding how to work with inverse sine functions and their properties.
  • Pythagorean Identity – Using the identity cos(x) = sqrt(1 - sin^2(x)) to find cosine values from sine values.
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