Question

Find the value of \[\operatorname{arc} \;cos(0)\].

Answer 1

Hint: This is based on the concept of inverse trigonometric functions. Trigonometric functions are related between angles and sides. \[\operatorname{arc} \;cos(0)\] means \[{\cos ^{ - 1}}\left( 0 \right)\], that is, find an angle whose cosine is \[0\].

Complete step by steps solution:
\[arc\] of a value means to find its inverse. Inverse trigonometric functions serve exactly the opposite of trigonometric operations, they are used to find an angle from any trigonometric ratios.
\[\cos \left( {\dfrac{\pi }{2}} \right) = 0\],
\[\therefore \] \[{\cos ^{ - 1}}\left( 0 \right)\] \[ = \] \[\dfrac{\pi }{2}\].
This is the principal value of the angle.
From general solution of \[\cos x\]:
\[\cos x = 0\]\[ \Rightarrow x = \left( {n\pi + \dfrac{\pi }{2}} \right)\], \[n \in I\].
Hence the other values of the angles can be obtained by substituting \[n\] with \[ \pm 1\], \[ \pm 2\],….
Other values are \[\dfrac{{3\pi }}{2}\] \[\left( {n = 1} \right)\], \[\dfrac{{5\pi }}{2}\] \[\left( {n = 2} \right)\], and so on.

Note:
Students must memorise the values of certain trigonometric angles \[\left( {{0^ \circ },{{30}^ \circ },{{45}^ \circ },{{60}^ \circ },{{90}^ \circ }} \right)\]. Students must be careful that the inverse trigonometric operation gives an angle and not any number. Be careful while putting the values and do not confuse between the values of sin and cosine.