question_answer

Domain and Range of \[{{\cos }^{-1}}x=\]

A) \[\left( -1,\,\,1 \right),\,\left( 0,\,\,\pi  \right)\]

B) \[\left[ -1,\,\,1 \right],\,\left( 0,\,\pi  \right)\]

C) \[\left[ -1,\,1 \right],\,\left[ 0,\,\,\pi  \right]\]

D) \[\left( -1,\,\,1 \right),\,\left[ -\frac{\pi }{2},\frac{\pi }{2} \right]\]

Correct Answer: C

Solution :

\[A{{B}^{2}}={{\left( AD \right)}^{2}}+{{\left( BD \right)}^{2}}={{\left( 30\sqrt{3} \right)}^{2}}+{{\left( 30 \right)}^{2}}\] \[=2700+900=3600\] \[\Rightarrow \,AB=60\,\,m\]. Domain of \[{{\cos }^{-1}}x=\left[ -1,1 \right]\] Range of \[{{\cos }^{-1}}x=\left[ 0,\,\,\pi  \right]\]