i figured out some just dont know how to do the rest

Question

(a) The unit circle is the circle centered at

with radius 2 .

(b) The equation of the unit circle is

x2+y2=12

.

(c) Suppose the point P(x, y) is on the unit circle. Find the missing coordinate.

(i)    

P 1, 4

(ii)    

P 5 , 1

(iii)    

P −1, 6

(iv)    

P 7 , −1

 

Answer 1

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 1 unit.

Step 2:

(b)

The standard form of circle 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 y -coordinate for .

Substitute in circle equation.

The point is .

(ii)

Find the value of x -coordinate for .

Substitute in circle equation.

The point is .

(iii)

Find the value of y -coordinate for .

Substitute in circle equation.

The point is .

(iv)

Find the value of x -coordinate for .

Substitute in circle equation.

The point is .

Solution:

(a) Center of the unit circle is and radius is 1 unit.

(b) Equation of unit circle is

(c)

(i) .

(ii) .

(iii) .

(iv) .