Basic Inverse Trigonometric Functions

Q.

If $si{n}^{-1}x=\frac{\pi }{5}$ for some $xϵ(-1,1),$ then the value of $co{s}^{-1}x$ is
[IIT 1992]

1. 
   

2. 
   

3. 
   

4. 
   

Q. If a function is invertible, then the function must be

1. One-to-One Function
2. Many - to - One function
3. On to function
4. Bijection

Q. Inverse is defined for every trigonometric function in its domain.

1. False
2. True

Q. The function y = cos x is one - to - one and onto in the interval $[\frac{-\pi }{2},\frac{\pi }{2}]$

1. True
2. False

Q.

\(sec^{-1}[sec(-30^\circ)]=\)
[MP PET 1992]

Q. $y=si{n}^{-1}\left(x\right)$ is the inverse of the function y=sin(x).

1. True
2. False

Q.

The principal value of $si{n}^{-1}\left[sin\left(\frac{2\pi }{3}\right)\right]$
[IIT 1986]

1. 
2. 
3. 
4. None of these

Q. $Ifx⩾1orx⩽-1,thencose{c}^{-1}\left(x\right)=$

1. None of these
2. $se{c}^{-1}(\frac{\pi }{2}-x)$
3. $si{n}^{-}1\left(\frac{1}{x}\right)$
4. $\frac{1}{si{n}^{-1}\left(x\right)}$

Q. If $si{n}^{-1}\left(sin\left(\frac{2x^2+4}{1+x^2}\right)\right)<\pi -3$

1. |x| < 1
2. |x|>1
3. $|x|\le 1$
4. $|x|\ge 1$

Q. f(x) = cos(x) defined on f : [a, b] $\to$ [-1, 1] has its inverse then which of the following is correct?

1. $a=-\pi ;b=\pi$
2. $a=0;b=\pi$
3. $a=0;b=2\pi$
4. None of these