Answer
(a) $A_{x}=0$ units, $A_{y}=+12$ units
(b) $A_{x}=-12$ units, $A_{y}=0$ units
(c) $A_{x}=0$ units, $A_{y}=-12$ units
(d) $A_{x}=+12$ units, $A_{y}=0$ units
Work Step by Step
Given, $|A|=12$ units
(a) The sizes of the $x$ and $y$ components of the vector for the rotational angle $90^{\circ}$:
$A_{x}=|A|\cos90^{\circ}=0$ units
$A_{y}=|A|\sin90^{\circ}=+12$ units
(b) The sizes of the $x$ and $y$ components of the vector for the rotational angle $180^{\circ}$:
$A_{x}=|A|\cos180^{\circ}=-12$ units
$A_{y}=|A|\sin180^{\circ}=0$ units
(c) The sizes of the $x$ and $y$ components of the vector for the rotational angle $270^{\circ}$:
$A_{x}=|A|\cos270^{\circ}=0$ units
$A_{y}=|A|\sin270^{\circ}=-12$ units
(d)The sizes of the $x$ and $y$ components of the vector for the rotational angle $360^{\circ}$:
$A_{x}=|A|\cos360^{\circ}=+12$ units
$A_{y}=|A|\sin360^{\circ}=0$ units
