Given a unit circle, what is the value of y in the first quadrant corresponding to an x-coordinate of 5/8?
In a unit circle, the
From SOH-CAH-TOA, we know that this means if we have a right triangle, the adjacent side is
We can find the
We can plug our values in to get
We know that sine is equal to opposite over the hypotenuse. We essentially just found the opposite side, so we can plug in to get
This is the
Hope this helps!
Picture a right triangle with corners made up of the point on the circle (whose x coordinate is 5/8) and the projections of that point on the x and y axes. The point on the x axis is 5/8 of the way from the origin to the circle. Since this is a unit circle, the hypotenuse by definition = 1.
where x and y are the coordinates of the spot on the unit circle and h is the length of the hypotenuse which, as I said, is 1.
Let the angle between a line from the origin to the spot on the unit circle be
It is given that x = 5/8.
I hope this helps,