Question

A metal plate has the form of a quarter circle with a radius of R = 106cm . Two 3 cm holes are to be drilled in the plater r = 95cm from the corner at 30 degrees and 60as shown above. To use a computer controlled milling machine you must know the Cartesian coordinates of the holes. Assuming the origin is at the corner what are the coordinates of the holes (x_{1}, y_{1}) and (x_{2}, y_{2}) ? Round your answer to 3 decimal places

Answer 1

`\begin{gathered} (x_1,y_1)--\gt(0.866,0.500) \\ (x_2,y_2)--\gt(0.500,0.866) \end{gathered}`

1) Considering that this quarter circle is one sector of the unit circle and that

`30^(\circ)=(\pi)/(6)`

2) Let's sketch this out to better grasp the idea:

Note that the first coordinate will be given by its cos(theta), and the second one by its sine(theta)

3) Based on that principle, we can tell the following:

`\begin{gathered} (x_1,y_1)--->(cos(30^(\circ)),\sin(30^(\circ)))=((√(3))/(2),(1)/(2)) \\ \\ (x_(2,)y_2)-->(\cos(60),\sin(60))=((1)/(2),(√(3))/(2)) \\ \end{gathered}`

As the holes need to be drilled by the machine, so we need to find approximations to those coordinates:

`\begin{gathered} (x_1,\:y_1)-->(0.866,0.500) \\ (x_2,y_2)-->(0.500,0.866) \end{gathered}`

Thus, these are the coordinates to be put into the computer.