This question is worded in a way to trick you so please read carefully. You CANNOT just calculate the x and y components of the electric field using the distances 3cm and 2cm, because you are not measuring the electric field at a distance of 3 or 2 cm away. These are the components of the distances that will help you find the total distance and the magnitude of the field at this location, and then the angle required to break the field into components, only AFTER you've found this magnitude.
Imagine a right triangle starting at the origin and the hypotenuse extending to (3cm,2cm), with base 3cm = 0.03m and height 2cm =0.02m.
Distance r = sqrt(0.03^2 + 0.02^2) = 0.036055 m
We will also use this triangle to extract the angle above the horizontal (the angle in the bottom left corner of the triangle) because this angle is the same angle of the direction of our electric field. For this we will use inverse tangent(y/x).
Theta = tan^-1 ( 0.02/0.03) = 33.69 degrees above the horizontal (north of east)
Now we can find the magnitude of the electric field at this distance:
Q = 4.5 micro C = 4.5 * 10^-6 C
Q is positive so we know the E field points away from the origin (up and to the right toward our point)
E = k Q / r^2
E magnitude = (8.99 * 10^9)(4.5 * 10^-6) / (0.036055)^2 = 31119231 N/C = 3.11 * 10^7 N/C
Now to find the components of the electric field, imagine the same right triangle we had before. This time, instead of finding the hypotenuse, we have the hypotenuse - it is the magnitude of the electric field we just found. We also have the angle theta = 33.69 degrees, and we are looking for the x and y components.
We will find the x and y components separately using cosine and sine, respectively.
E x-component = Emagnitude * cos(theta) = 3.11*10^7 * cos(33.69) = 2.59*10^7 N/C pointing to the right
E y-component = Emagnitude * sin(theta) = 3.11*10^7 * sin(33.69) = 1.75* 10^7 N/C pointing up
