Question

Convert (1,1) to polar form

Answer 1

Polar form : ( √2 , 45°).

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).

Answer 2

Polar form: (√2, 45°)

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=√(1+1)\\ r=√(2)`

`\alpha=tan^(-1) ((y)/(x))`

Replacing the known values:

`\alpha =tan^(-1) ((1)/(1))\\ \alpha=tan^(-1) (1)\\ \alpha=45^(\°)`

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