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Unit Circle



The set of factors at a distance 1 from the origin is a circle of radius 1. 

The unit circle is the circle of radius 1 centered on the origin within the xy-plane.

Its equation is

x2 + y2  =  1

A Level on the Unit Circle

Instance 1 :

Present that the purpose A(4/5, -3/5) is on the unit circle. 

Answer : 

Now we have to indicate that this level satisfies the equation of the unit circle, that’s, x2 + y2 = 1. 

(4/5)2 + (-3/5)2  =  16/25 + 9/25

=  (16 + 9)/25

=  25/25

=  1

So, A is on the unit circle. 

Instance 2 :

Present that the purpose B(√3/3, √6/3) is on the unit circle. 

Answer : 

Now we have to indicate that this level satisfies the equation of the unit circle, that’s, x2 + y2 = 1. 

(√3/3)2 + (√6/3)2  =  3/9 + 6/9

=  (3 + 6)/9

=  9/9

=  1

So, P is on the unit circle. 

Finding a Level on the Unit Circle

Instance 3 :

The purpose P is on the unit circle. Discover P(x, y) from the given data. The y-coordinate of P is -1/3 and the x-coordinate is constructive.

Answer :

As a result of the purpose is on the unit circle, now we have 

x2 + (-1/3)2  =  1

x+ 1/9  =  1

Subtract 1/9 from all sides.

x2  =  1 – 1/9

x2  =  9/9 – 1/9

x2  =  (9 – 1)/9

x2  =  8/9

Take sq. root on either side. 

x  =  ± 2√2/3

As a result of x-coordinate is detrimental, 

x  =  2√2/3

The purpose is 

P(2√2/3, -1/3)

Instance 4 :

If the the purpose P(√3/2, ok) is on the unit circle in quadrant IV, discover P(x, y).   

Answer : 

As a result of the purpose is on the unit circle, now we have 

(√3/2)2 + ok2  =  1

3/4 + ok2  =  1

Subtract 3/4 from all sides.

ok2  =  1 – 3/4

ok2  =  4/4 – 3/4

ok2  =  (4 – 3)/4

ok2  =  1/4

Take sq. root on either side. 

ok  =  ± 1/2

As a result of the purpose is in quadrant IV and ok is the y-coordinate, the worth of ok have to be detrimental. 

ok = -1/2

The purpose is 

P(√3/2-1/2)

Instance 5 :

The purpose P is on the unit circle. Discover P(x, y) from the given data. The x-coordinate of P is -2/5 and P lies above the x-axis.

Answer : 

As a result of the purpose is on the unit circle, now we have 

(-2/5)2 + y2  =  1

4/25 + y2  =  1

Subtract 4/25 from all sides.

y2  =  1 – 4/25

y2  =  25/25 – 4/25

y2  =  (25 – 4)/25

y2  =  21/25

Take sq. root on either side. 

y  =  ± 21/5

As a result of P lies above the x-axis, y-coordinate have to be constructive.

y  =  21/5

The purpose is 

P(-2/5, 21/5)

Instance 6 :

The purpose P is on the unit circle. Discover P(x, y) from the given data. The y-coordinate of P is -1/2 and P lies on the left aspect of y-axis.

Answer : 

As a result of the purpose is on the unit circle, now we have 

x2 + (-1/2)2  =  1

x+ 1/4  =  1

Subtract 1/4 from all sides.

x2  =  1 – 1/4

x2  =  4/4 – 1/4

x2  =  (4 – 1)/4

x2  =  3/4

Take sq. root on either side. 

x  =  ± √3/2

As a result of P lies on the left aspect of y-axis, x-coordinate have to be detrimental.

x  =  –√3/2

The purpose is 

P(√3/2-1/2)

Associated Stuff

1. Terminal Factors on the Unit Circle

2. Reference Quantity on the Unit Circle

3. Utilizing Reference Quantity to Discover terminal Factors 

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