Q. 4 - Calculus

Question

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

A graph is symmetrical with respect to the x-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 $(r,-\theta )$

Step 1. Given information

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

Step 2. Find the point.

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

The graph is symmetrical with respect to the x-axis if, for every point $(r,\theta )$ on the graph,the point is $(r,-\theta )$ also on the graph: