Question:
The minimum value of \( 1 - \sin x \) is:
The minimum value of \( 1 - \sin x \) is:
Show 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.
Updated On: Jan 13, 2026
- \( -1 \)
- \( 1 \)
- \( 2 \)
- \( 0 \)
Show Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
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).
Was this answer helpful?
0
1
Top KCET Mathematics Questions
- If $a, b$ and $c \in N$ which one of the following is not true ?
- If $a | (b + c)$ and $a| (b-c)$ where $a,b,c \in \, N $ then
- For the parabola $y^2 = 4x$, the point $P$ whose focal distance is $17$, is
- $G = \left\{\begin{bmatrix} x&x \\[0.3em] x & x \end{bmatrix} , x \text{ is a nonzero real number} \right\}$ is a group with respect to matrix multiplication. In this group, the inverse of $\begin{bmatrix} \frac{1}{3} &\frac{1}{3} \\[0.3em] \frac{1}{3} & \frac{1}{3} \end{bmatrix}$ is
- How many $5$ digit telephone numbers can be constructed using the digits $0$ to $9$, if each number starts with $67$ and no digit appears more than once ?
View More Questions
Top KCET Inverse Trigonometric Functions Questions
- If $\frac {3x+1}{(x-1)(x+3)} =\frac {A}{x-1} + \frac {B} {x+3} \sin^{-1} \frac {A}{B}$ = is equal to
- If $a > b > 0, Sec^{-1} \left(\frac{a+b}{a-b} \right)= 2 \; Sin^{-1}x $ then $x = $ _____
- If $a > b > 0$, then the value of $Tan^{-1} \left(\frac{a}{b}\right)+Tan^{-1}\left(\frac {a+b}{a-b}\right) $
- If $\frac {(x+1)^2}{x^3+x}=\frac {A}{x}+\frac {Bx+C}{x^2+1}$, then $\sin^{-1} \,A + \tan ^{-1} \,B + sec ^{-1} \,C$ is equal to
- If $\sin^{-1} \, x + \sin^{-1} \,y= \frac{\pi}{2}$ , then $x^2$ is equal to
View More Questions
Top KCET Questions
- Which of the following is not true for oxidation?
- If $a, b$ and $c \in N$ which one of the following is not true ?
- When $50\, cm ^{3}$ of $0.2\, N$ $H_{2} SO _{4}$ is mixed with $50 cm ^{3}$ of $1 N\, KOH$, the heat liberated is :
- If $a | (b + c)$ and $a| (b-c)$ where $a,b,c \in \, N $ then
- Which of the following is NOT a pair of functional isomers?
View More Questions