Question

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

Answer 1

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,

& x=r\cos \theta \\\ & y=r\sin \theta \\\ \end{aligned}$$ We can now substitute the value of r and $$\theta $$ in the above formula, we get $$\begin{aligned} & \Rightarrow x=0\cos \left( \dfrac{\pi }{6} \right) \\\ & \Rightarrow y=0\sin \left( \dfrac{\pi }{6} \right) \\\ \end{aligned}$$ We can now simplify the above step, as we multiply any number with 0, the answer will be zero. $$\begin{aligned} & \Rightarrow x=0 \\\ & \Rightarrow y=0 \\\ \end{aligned}$$ We can see that this could have been solved by just noting that the radius is zero and this means we are at the origin. **Therefore, the rectangular coordinates are $$\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.