Problem 88 - Algebra and Trigonometry

Question

Explain how to plot \((r, \theta)\) if \(r>0\) and \(\theta>0\)

Step-by-Step Solution

Answer

To plot the polar coordinate point (r, θ) where r > 0 and θ > 0, first identify the 'r' value and measure this distance from the origin. From that point, rotate counter-clockwise 'θ' degrees or units. The point you land on is your polar coordinate (r, θ).

Step 1: Understand Polar Coordinate System

Polar coordinates are two-dimensional and thus they can be used to determine the coordinates of a point in the XY-plane. Where r is the radial distance and θ is the angular coordinate. It's vital to first grasp these concepts before proceeding to plot (r, θ).

Step 2: Determine the Values of r and θ

Given that both r and θ are more than 0, determine these two values. 'r' is a positive radial distance from the origin, and 'θ' is a positive angle in degrees (or radians) measured counter-clockwise from the x-axis.

Step 3: Plot the Polar Coordinate

Next is the actual plotting of the polar coordinate. First, measure 'r' units away from the origin. From that point, move counter-clockwise from the x-axis 'θ' units (or degrees). Mark the location - that's the polar coordinate point (r, θ).