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If sin^(-1)(x) = π/4, what is the value of x?

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Question: If sin^(-1)(x) = π/4, what is the value of x?

Options:

  1. 1/2
  2. √2/2
  3. 1
  4. 0

Correct Answer: √2/2

Solution: 

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

If sin^(-1)(x) = π/4, what is the value of x?

Practice Questions

Q1
If sin^(-1)(x) = π/4, what is the value of x?
  1. 1/2
  2. √2/2
  3. 1
  4. 0

Questions & Step-by-Step Solutions

If sin^(-1)(x) = π/4, what is the value of x?
  • Step 1: Understand that sin^(-1)(x) means the angle whose sine is x.
  • Step 2: The equation sin^(-1)(x) = π/4 tells us that the sine of some angle is equal to x.
  • Step 3: Recognize that π/4 is a specific angle (45 degrees) in trigonometry.
  • Step 4: Find the sine of π/4. We know that sin(π/4) = √2/2.
  • Step 5: Since sin^(-1)(x) = π/4, we can say that x = sin(π/4).
  • Step 6: Therefore, x = √2/2.
  • Inverse Trigonometric Functions – Understanding how to solve for x when given an inverse sine function.
  • Trigonometric Values – Knowledge of the sine values for common angles, particularly π/4.
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