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

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Question: If x = sin^(-1)(1/√2), then what is the value of cos^(-1)(x)?

Options:

  1. π/4
  2. π/3
  3. π/2
  4. π/6

Correct Answer: π/4

Solution: 

Since x = sin^(-1)(1/√2) = π/4, then cos^(-1)(x) = π/2 - π/4 = π/4.

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

Practice Questions

Q1
If x = sin^(-1)(1/√2), then what is the value of cos^(-1)(x)?
  1. π/4
  2. π/3
  3. π/2
  4. π/6

Questions & Step-by-Step Solutions

If x = sin^(-1)(1/√2), then what is the value of cos^(-1)(x)?
Correct Answer: π/4
  • Step 1: Understand that sin^(-1)(1/√2) means we are looking for an angle whose sine is 1/√2.
  • Step 2: Recall that sin(π/4) = 1/√2. Therefore, x = sin^(-1)(1/√2) = π/4.
  • Step 3: Now we need to find cos^(-1)(x), which means we are looking for an angle whose cosine is x (which we found to be π/4).
  • Step 4: Use the identity cos^(-1)(x) + sin^(-1)(x) = π/2. Since x = π/4, we can substitute: cos^(-1)(π/4) = π/2 - π/4.
  • Step 5: Calculate π/2 - π/4, which equals π/4.
  • Inverse Trigonometric Functions – Understanding the relationship between sine and cosine through their inverse functions.
  • Angle Relationships – Using the complementary angle relationship between sine and cosine.
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