Question

Help asap, ​please. Thanks

Answer 1

Explanation:

The relationship between rectangular form and polar form is given as follows:-

`x=r*cos\theta, \;and\; y=r*sin\theta`

Part A: x=2

`x=2\\r*cos\theta=2\\r=2/cos\theta\\r=2sec\theta`

Part B: x² + y² = 36

`x^2+y^2=36\\(r*cos\theta)^2+(r*sin\theta)^2=36\\r^2*cos^2\theta+r^2*sin^2\theta=36\\r^2*(cos^2\theta+sin^2\theta)=36\\r^2*(1)=36\\r^2=36\\r=6`

Part C: x² + y² = 2y

`x^2+y^2=2y\\(r*cos\theta)^2+(r*sin\theta)^2=2(r*sin\theta)\\r^2*(cos^2\theta+sin^2\theta)=2*r*sin\theta\\r^2=2*r*sin\theta\\r=2sin\theta`

Part D: x = √3 y

`x = √(3) y \\ r*cos\theta=√(3)*r*sin\theta\\ cos\theta/sin\theta=√(3)\\cot\theta=√(3)\\\theta=cot^(-1)(√(3))\\\theta=\pi/6`

Part E: x = y

`x=y\\r*cos\theta=r*sin\theta\\cos\theta=sin\theta\\sin\theta/cos\theta=1\\tan\theta=1\\\theta=tan^(-1)(1)\\\theta=\pi/4`