Convert from rectangular quantities into polar form

Question

I need help with these three problems. Thank you so much.

Answer 1

(1)

Step 1 :

Conversion from rectangular to polar equation :

and

(a)

The rectangular equation is .

Substitute  in polar equation.

Find magnitude.

Find angle.

The polar equation is

(b)

The rectangular equation is .

Substitute  in polar equation.

Find magnitude.

Find angle.

The polar equation is

Solution :

(a) The polar equation is

(b) The polar equation is

Answer 2

(2)

Step 1 :

Conversion from Polar to rectangular equation :

and .

(a)

The polar form is

Substitute in the rectangular equation.

The rectangular form is

(b)

The polar form is

Substitute in the rectangular equation.

The rectangular form is

(c)

The polar form is

Substitute in the rectangular equation.

The rectangular form is

Solution :

(a) The rectangular form is

(b) The rectangular form is

(c) The rectangular form is

Answer 3

(3)

Step 1 :

The expression is , Where,

Conversion from Polar to rectangular equation :

and .

(i)

The polar form is

Substitute in the rectangular equation.

(ii)

The polar form is

Substitute in the rectangular equation.

(iii)

The polar form is

Substitute in the rectangular equation.

Find the value of .

Convert into polar form is

Solution :

The resulting phasor in polar form is