Step 1:

\

(a)

\

The unit circle is the circle with its center at the origin $\"\"$ and a radius of one unit.

\

Center of the unit circle is $\"\"$ and radius is $\"\"$ unit.

\

Step 2:

\

(b)

\

The standard form of line equation is $\"\"$ .

\

For an unit circle: $\"\"$ and $\"\"$ .

\

Substitute the corresponding values in standard form.

\

$\"\"$

\

$\"\"$

\

Equation of unit circle is $\"\"$

\

Step 3:

\

(c)

\

(i)

\

The point $\"\"$ lies on the unit circle.

\

Equation of unit circle is $\"\"$

\

Find the value of missing coordinate.

\

Find the value of $\"\"$ -coordinate for $\"\"$ .

\

Substitute $\"\"$ in circle equation.

\

$\"\"$

\

The point is $\"\"$ .

\

(ii)

\

The point $\"\"$ lies on the unit circle.

\

Equation of unit circle is $\"\"$

\

Find the value of missing coordinate.

\

Find the value of $\"\"$ -coordinate for $\"\"$ .

\

Substitute $\"\"$ in circle equation.

\

$\"\"$

\

The point is $\"\"$ .

\

(iii)

\

The point $\"\"$ lies on the unit circle.

\

Equation of unit circle is $\"\"$

\

Find the value of missing coordinate.

\

Find the value of $\"\"$ -coordinate for $\"\"$ .

\

Substitute $\"\"$ in circle equation.

\

$\"\"$

\

The point is $\"\"$ .

\

(iv)

\

The point $\"\"$ lies on the unit circle.

\

Equation of unit circle is $\"\"$

\

Find the value of missing coordinate.

\

Find the value of $\"\"$ -coordinate for $\"\"$ .

\

Substitute $\"\"$ in circle equation.

\

$\"\"$

\

The point is $\"\"$ .

\

Solution:

\

(a) Center of the unit circle is $\"\"$ and radius is $\"\"$ unit.

\

(b) Equation of unit circle is $\"\"$

\

(c)

\

(i) $\"\"$ .

\

(ii) $\"\"$ .

\

(iii) $\"\"$ .

\

(iv) $\"\"$ .

\

\

Step 1:

\

\

(a)

\

The unit circle is the circle with its center at the origin $\"\"$ and a radius of one unit.

\

Center of the unit circle is $\"\"$ and radius is $\"\"$ unit.

\

Step 2:

\

\

(b)

\

The standard form of line equation is $\"\"$ .

\

For an unit circle: $\"\"$ and $\"\"$ .

\

Substitute the corresponding values in standard form.

\

$\"\"$

\

$\"\"$

\

Equation of unit circle is $\"\"$

\

Step 3: \ \

\

(c) \ \

\

(i)

\

The point $\"\"$ lies on the unit circle.

\

Equation of unit circle is $\"\"$

\

Find the value of missing coordinate.

\

Find the value of $\"\"$ -coordinate for $\"\"$ .

\

Substitute $\"\"$ in circle equation.

\

$\"\"$

\

The point is $\"\"$ .

\

(ii)

\

The point $\"\"$ lies on the unit circle.

\

Equation of unit circle is $\"\"$

\

Find the value of missing coordinate.

\

Find the value of $\"\"$ -coordinate for $\"\"$ .

\

Substitute $\"\"$ in circle equation.

\

$\"\"$

\

The point is $\"\"$ .

\

(iii)

\

The point $\"\"$ lies on the unit circle.

\

Equation of unit circle is $\"\"$

\

Find the value of missing coordinate.

\

Find the value of $\"\"$ -coordinate for $\"\"$ .

\

Substitute $\"\"$ in circle equation.

\

$\"\"$

\

The point is $\"\"$ .

\

(iv)

\

The point $\"\"$ lies on the unit circle.

\

Equation of unit circle is $\"\"$

\

Find the value of missing coordinate.

\

Find the value of $\"\"$ -coordinate for $\"\"$ .

\

Substitute $\"\"$ in circle equation.

\

$\"\"$

\

The point is $\"\"$ .

\

Solution:

\

(a) Center of the unit circle is $\"\"$ and radius is $\"\"$ unit.

\

(b) Equation of unit circle is $\"\"$

\

(c)

\

(i) $\"\"$ .

\

(ii) $\"\"$ .

\

(iii) $\"\"$ .

\

(iv) $\"\"$ . \ \