Question

I don’t know how to do this one.

Answer 1

(a) The unit circle is centered at (0,0) with a radius of 1.

(b) The equation of a circle of radius r, with a center located at (0,0):

x²+ y² = r².

(c) (i) P(1,0)

(ii) P(0,1)

(iii) P(-1,0)

(iv) P(0,-1)

Step-by-step explanation:

Answer 2

Part (a)

The unit circle is centered at (0,0). This point is the origin.

The radius of the unit circle is 1

The term "unit" means "one", which describes the radius length.

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Part (b)

The equation of the unit circle is x^2+y^2 = 1

The general equation of any circle is (x-h)^2+(y-k)^2 = r^2

In this case, the unit circle has center (h,k) = (0,0) and radius r = 1.

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Part (c)

The following four points are on the unit circle

• (1,0)
• (0,1)
• (-1,0)
• (0,-1)

As shown below in the diagram. The idea is to plug each given coordinate into the equation from part (b), and solve for the missing variable.

For example, if we know x = 1, then...

x^2+y^2 = 1

1^2+y^2 = 1

1+y^2 = 1

y^2 = 1-1

y^2 = 0

y = sqrt(0)

y = 0

Meaning x = 1 leads to y = 0. So (x,y) = (1,0) is one point on the circle. The other parts are handled in a similar fashion.