Question

Select the correct answer. Convert (1, 1) to polar form. A. (2, 45°) B. (1, 45°) C. (2, 225°) D. (, 45°)

Answer 1

(sqrt(2),45°)

Explanation:

because norm of(1,1)=sqrt(1^2+1^2)=sqrt(2)

angle=arctan(1/1)=45°

Answer 2

(√2,45°)

Explanation:

Here you are required to convert (x,y) to (r,Ф)

`r=√(x^2+y^2)`

Ф= tan⁻¹ (y/x)

Given x=1 and y=1

`r=√(1^2+1^2) \\\\\\r=√(1+1) =√(2)`

(1,1) is in the 1st quadrant thus Ф should be in the 1st quadrant too

Ф=tan⁻¹ (1) =45°

Hence (1,1) in polar form is (√2,45°)