Question

The minimum value of \( 1 - \sin x \) is:

• A. \( -1 \)
• B. \( 1 \)
• C. \( 2 \)
• D. \( 0 \)

Hint:

For functions like \( 1 - \sin x \), always remember that the sine function has a maximum value of 1 and a minimum value of -1. Use these bounds to find the range of the function.

Answer 1

The Correct Option is D

We are given: \[ -1 \leq \sin x \leq 1 \] Now, \[ 1 - \sin x \geq 0 \quad \text{(since \( \sin x \leq 1 \))} \] \[ 1 + 1 \geq \sin x + 1 \geq 1 - 1 \] \[ 0 \leq 1 - \sin x \leq 2 \] Thus, the minimum value of \( 1 - \sin x \) is \( 0 \), which corresponds to option (4).