Question

How do you write the equation `4=rcos(theta+pi/4)` in rectangular form?

Answer 1

The equation is `x-y=4sqrt2`

Explanation:

We use,

`cos(a+b)=cosacosb-sinasinb`

`cos(theta+pi/4)=costhetacos(pi/4)-sinthetasin(pi/4)`

`cos(pi/4)=sin(pi/4)=sqrt2/2`

The conversion from polar coordnates to cartesian coordinates is made with the following equations

`x=rcostheta`

and `y=rsintheta`

We can transform the above equation,

`4=rcos(theta+pi/4)=rcosthetacos(pi/4)-rsinthetasin(pi/4)`

`4=xsqrt2/2-ysqrt2/2`

`4sqrt2=x-y`