Question

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

Answer 1

Answer:

y = 0.8425   or   y = -0.8425

Step-by-step 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...

$\sqrt{y^2}=\pm \sqrt{0.70980231}$

$y=\pm 0.8424976171...$

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.