Suppose that (5/13,y) is a point in Quadrant IV lying on the unit circle. Find y. Write the exact value not a decimal approximation
-12/13?
think of the 5-12-13 right triangle.
In QIV, y is negative
So, what do you think?
correct.
To find the value of y, we need to utilize the properties of the unit circle and the coordinates given.
In Quadrant IV, the x-coordinate is positive, and the y-coordinate is negative. Since (5/13, y) lies on the unit circle, we know that the radius of the circle is 1.
Using the Pythagorean theorem, we can find the value of y. The Pythagorean theorem states that for any point (x,y) on the unit circle, the equation x^2 + y^2 = r^2 holds true, where r is the radius (which is 1 in this case).
We have the x-coordinate (5/13), and by substituting it into the Pythagorean theorem equation, we get:
(5/13)^2 + y^2 = 1^2
25/169 + y^2 = 1
To solve for y, we subtract 25/169 from both sides of the equation:
y^2 = 1 - 25/169
y^2 = (169 - 25)/169
y^2 = 144/169
Taking the square root of both sides, we find:
y = ± √(144/169)
Since we are in Quadrant IV and the y-coordinate is negative, we can conclude that y = -√(144/169).
Therefore, the exact value of y is -√(144/169).