\

Step 1 :

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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 $\"\"$

\

(2)

\

Step 1 :

\

Conversion from Polar to rectangular equation :

\

$\"image\"$ and $\"image\"$ .

\

(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 $\"\"$

\

(3)

\

Step 1 :

\

Conversion from Polar to rectangular equation :

\

$\"image\"$ and $\"image\"$ .

\

The expression is $\"\"$ , Where, $\"\"$

\

(a)

\

The polar form is $\"\"$

\

Substitute $\"\"$ in the rectangular equation. \ \

\

$\"\"$

\

$\"\"$

\

(b)

\

The polar form is $\"\"$

\

Substitute $\"\"$ in the rectangular equation. \ \

\

$\"\"$

\

$\"\"$

\

(c)

\

The polar form is $\"\"$

\

Substitute $\"\"$ in the rectangular equation. \ \

\

$\"\"$

\

$\"\"$

\

Find the value of $\"\"$ .

\

$\"\"$

\

$\"\"$

\

Converte in to polar form is

\

$\"\"$

\

Solution :

\ The resulting phasor in polar form is

\"\"