Question

How do you convert \[\left( 0,\dfrac{\pi }{6} \right)\] to rectangular form?

Answer 1

Hint: In this problem, we have to convert the given polar form to the rectangular form. We are given a polar coordinate to convert them into a rectangular coordinate. We can use the conversion formula to convert from polar coordinates to rectangular coordinates. We can substitute the value of r and \[\theta \] in the conversion formula which is given in this problem as polar coordinate, to find the rectangular coordinates.

Complete step by step solution:
We know that the given polar coordinates are,
\[\left( 0,\dfrac{\pi }{6} \right)\]
Where, r = 0, \[\theta =\dfrac{\pi }{6}\]
We know that the conversion formula to convert from polar coordinates to rectangular coordinates is,
\[\begin{align}
  & x=r\cos \theta \\
 & y=r\sin \theta \\
\end{align}\]
We can now substitute the value of r and \[\theta \] in the above formula, we get
\[\begin{align}
  & \Rightarrow x=0\cos \left( \dfrac{\pi }{6} \right) \\
 & \Rightarrow y=0\sin \left( \dfrac{\pi }{6} \right) \\
\end{align}\]
We can now simplify the above step, as we multiply any number with 0, the answer will be zero.
\[\begin{align}
  & \Rightarrow x=0 \\
 & \Rightarrow y=0 \\
\end{align}\]
We can see that this could have been solved by just noting that the radius is zero and this means we are at the origin.
Therefore, the rectangular coordinates are \[\left( 0,0 \right)\].

Note: Students make mistakes while writing the conversion formula to convert from polar form to a rectangular form, we should know that the polar coordinates are given as \[\left( r,\theta \right)\] format. We should know that in case we are given a number instead of 0, then we will have to find the trigonometric values for the given degree and we have to solve for x and y coordinates.