Find 4 points on the unit circle which have either a x- or y- coordinate equal to 1/ 3 . Then find all points on the unit circles whose x- and y- coordinates add up to 1/ 3 .

Answer 1

The equation of the unit circle is x² + y² = 1.

If we let x=1/3 and solve for y we will have 2 points where the x-coordinate is 1/3.

Similarly if y = 1/3, solving for x will give 2 more points where y-coordinate is 1/3.

For example:

1/9 + y²=1

y²=8/9

y = ±(2√2)/3

To find points on the unit circle where x and y coordinates sum to 1/3, find the points of intersection of the unit circle with the equation x + y = 1/3.

That means y = 1/3-x

Substituting:

x²+(1/3-x)²= 1/3

You can find exact values for x (this is a quadratic equation) by squaring the binomial combining similar terms, setting equal to zero in the process, and using the quadratic formula.

Try all of the above and check you solutions here:

desmos.com/calculator/puhldjl8iz