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

User Birlla
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1 Answer

6 votes
6 votes

Answer:

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.

User Sadak
by
3.4k points