Q. 5 - Calculus

Question

Fill in the blanks to convert between rectangular coordinates and polar coordinates. 

$x=.........$

Step-by-Step Solution

Answer

The value of $x=r\cos \theta$

Step 1. Given information

The horizontal distance of a point from y-axis is $x$

Step 2. Convert x into polar form:

Draw a diagram of a circle of radius $r$ and let a point $P(x,y)$ on the circle:

Apply trigonometric formula of cosine in the right angle triangle,

$$\begin{gathered} \cos \theta =\frac{x}{r} \\ x=r\cos \theta \end{gathered}$$