if the point (3/5,4/5) corresponds to an angle È in the unit circle, what is tan È?
tan E = y/x = (4/5) / (3/5) = 4/3
To find the value of tan(È), we need to know the coordinates of the point where an angle of È intersects the unit circle.
The unit circle is a circle with a radius of 1 centered at the origin (0,0) in the coordinate plane. It allows us to relate angles to points on the circle.
To determine the coordinates of a point on the unit circle corresponding to an angle È, we use trigonometric ratios.
The angle È is formed with the positive x-axis in a counterclockwise direction. So, if we draw a line from the origin (center of the unit circle) to the point (3/5, 4/5), it will intersect the circle at the point corresponding to angle È.
The horizontal distance from the origin to the point (3/5, 4/5) is indicated by the x-coordinate, which is 3/5. The vertical distance is indicated by the y-coordinate, which is 4/5.
To find the hypotenuse, we use the Pythagorean theorem, which states that the sum of the squares of the lengths of the two legs of a right triangle is equal to the square of the length of the hypotenuse.
In this case, the hypotenuse is the radius of the unit circle, which is 1. Therefore, we have:
(3/5)^2 + (4/5)^2 = 1^2
9/25 + 16/25 = 1
25/25 = 1
So, the point (3/5, 4/5) is indeed on the unit circle.
Now, we can calculate the value of tan(È) using the y-coordinate (4/5) divided by the x-coordinate (3/5):
tan(È) = (4/5) / (3/5) = (4/5) * (5/3) = 4/3
Therefore, tan(È) = 4/3.