Question

Convert (1,1) to polar form

Answer 1

Answer:

Polar form: (√2, 45°)

Step-by-step explanation:

Rectangular form: (1,1)=(x,y)→x=1, y=1

Polar form: (r,α)

$r=\sqrt{x^{2}+ y^{2} }$

Replacing the known values:

$r=\sqrt{1^{2}+1^{2} }\\ r=\sqrt{1+1}\\ r=\sqrt{2}$

$\alpha=tan^{-1} (\frac{y}{x})$

Replacing the known values:

$\alpha =tan^{-1} (\frac{1}{1})\\ \alpha=tan^{-1} (1)\\ \alpha=45^{\°}$

Then, the polar form is: (r,α)=(√2,45°)

Answer 2

Answer:

Polar form : ( √2 , 45°).

Step-by-step explanation:

Rectangular form is given

( 1 ,1 ) where x = 1, y = 1 .

General form of polar form is ( r , θ ).

r = √x²+y²

r = √1²+1²=√1+1=√2

θ = tan⁻¹(y/x)

θ= tan⁻¹(1/1)

θ= tan⁻¹(1)

θ = 45°

So, the polar form is (√2 , 45).