Question

Determine an approximate value for y if the coordinate (-0.5387 ,y) is on the unit circle

Answer 1

y = 0.8425 or y = -0.8425

Explanation:

All points in the Cartesian coordinate system have an x and y coordinate, defined by two perpendicular measurements.

If the point is on the unit circle, then the radius of the circle is defined to be 1 unit, and the corresponding right triangle follows the Pythagorean Theorem.

`a^2+b^2=c^2`

For a unit circle:

`x^2+y^2=1^2`

Substituting the known value for x, and simplifying...

`(-0.5387)^2+y^2=(1)^2`

`0.29019769+y^2=1`

Subtracting 0.29019769 from both sides to begin to isolate "y"...

`y^2=1-0.29019769`

`y^2=0.70980231`

Applying the square root property...

`√(y^2)=\pm √(0.70980231)`

`y=\pm 0.8424976171...`

So, (to 4 decimal places), the y coordinate could be either 0.8425 or -0.8425.

With only the given information, either result is a valid answer.