Question

WILL MAKE YOU BRAINLIEST!!!!!

Answer 1

The answer is y/x=1
The image shown is a Unit circle
And if theta is pi/4 than the (x,y) coordinates of that point will both be sqrt2/2
If you divide a number by itself it equals 1

Answer 2

Answer: The correct option is (D) $\dfrac{y}{x}=1.$

Step-by-step explanation:  We are given to select the correct option that is true of the values of x and y in the diagram.

We can see from the figure that

the polar co-ordinates of the point (x, Y) are given by

$r=1,~~~\theta=\dfrac{\pi}{4}.$

The relation between the Cartesian and polar co-ordinates are as follows :

$x^2+y^2=r^2~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\\tan^{-1}\dfrac{y}{x}=\theta~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

Substituting the values of polar co-ordinates of the given point i the above equations, we get

$x^2+y^2=1^2\\\\\Rightarrow x^2+y^2=1,$

and

$\tan^{-1}\dfrac{y}{x}=\dfrac{\pi}{4}\\\\\\\Rightarrow \dfrac{y}{x}=\tan\dfrac{\pi}{4}\\\\\\\Rightarrow \dfrac{y}{x}=1.$

So, we get two equations :

$x^2+y^2=1,~~~\dfrac{y}{x}=1.$

Since first equation is not in the given options, so the correct one is

(D) $\dfrac{y}{x}=1.$