Q. 5 - Calculus

Question

Fill in the blanks to complete each of the following theorem statements: 

A graph is symmetrical with respect to the y-axis if, for every point (r, θ) on the graph, the point ................is also on the graph. 

Step-by-Step Solution

Answer

The blank is filled by $\left(-r,-\theta \right)$.

Step 1. Given information

The graph is symmetrical about y-axis for every point  $\left(r,\theta \right)$

Step 2. Find the point.

As we know that the coordinates of the point $\left(r,\theta \right)$ means the distance of the point from origin is $r$ and the angle made by positive x-axis is $\theta$.

A graph is symmetrical with respect to the y-axis if, for every point (r, θ) on the graph, the point $\left(-r,-\theta \right)$  is also on the graph.