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

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

Options:

  1. -Ï€/6
  2. π/6
  3. -Ï€/3
  4. π/3

Correct Answer: -Ï€/6

Solution: 

sin^(-1)(-1/2) = -Ï€/6, since sin(-Ï€/6) = -1/2.

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

Practice Questions

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

Questions & Step-by-Step Solutions

If x = sin^(-1)(-1/2), then what is the value of x?
Correct Answer: -Ï€/6
  • Step 1: Understand that sin^(-1)(y) means 'what angle has a sine of y'.
  • Step 2: In this case, we need to find the angle whose sine is -1/2.
  • Step 3: Recall that the sine function is negative in the third and fourth quadrants.
  • Step 4: The angle that has a sine of 1/2 is Ï€/6 (or 30 degrees).
  • Step 5: Since we need the sine to be -1/2, we look for the angle in the fourth quadrant, which is -Ï€/6 (or -30 degrees).
  • Step 6: Therefore, x = sin^(-1)(-1/2) = -Ï€/6.
  • Inverse Trigonometric Functions – Understanding how to evaluate the inverse sine function and its range.
  • Quadrants of Trigonometric Functions – Recognizing the signs of sine in different quadrants to determine the correct angle.
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