Question

How to convert polar to rectangular form

Answer 1

POLAR COORDINATES

USING POLAR COORDINATES WE MARK A POINT BY HOW FAR AWAY AND WHAT ANGLE IT IS

CONVERTING

TO CONVERT FROM ONE TO THE OTHER WE WILL US THE TRIANGLE

Answer 2

To convert the polar equation into rectangular form, the following steps to be done  

Step 1:  

Rewrite the given trigonometric functions into sinθ,cosθ and tanθ

For example: To convert the polar equation r= 5 secθ into rectangular form  

Step 1:  

Rewrite secθ into cosθ

secθ=$\frac{1}{cos\ \theta}$  

Substituting this in the given polar equation

r=$\frac{5}{cos\ \theta}$  

Step 2:  

Change the above equation into rectangular form by substituting x=rcosθ,y=rsinθ.

Here, the applicable rectangular substitution is x=rcosθ

So, from step 1

$r=\frac{5}{cos\ \theta}$

Multiplying both sides by 1r

$\frac rr=\frac{5}{rcos\ \theta}$

Step 3:  

Substituting the value of r cosθ and simplify the equation

From step 2 we obtain 1=$\frac{5}{cos\ \theta}$

Substitute the value of rcosθ=x

1=$\frac 5x$  

By simplifying  

∴x=5  

Hence the given polar equation r=$\frac{5}{rsec\ \theta}$ is converted into rectangular form