If (a, b) is a point on the unit circle that corresponds to the angle t, then tan(t) equals:
by definition,
tan(t) = b/a
To find the value of tan(t) for a given point (a, b) on the unit circle, we need to use the trigonometric relationship between the tangent function and the coordinates of the point.
First, let's understand the unit circle. The unit circle is a circle with a radius of 1 centered at the origin (0, 0) in the coordinate plane. The angle t is measured in radians counterclockwise from the positive x-axis to the line connecting the origin to the point (a, b) on the unit circle.
The coordinates of the point (a, b) on the unit circle can be expressed as (cos(t), sin(t)). So, we have:
a = cos(t)
b = sin(t)
To find tan(t), we divide sin(t) by cos(t) because tan(t) = sin(t) / cos(t). Substituting the values of a and b, we get:
tan(t) = sin(t) / cos(t) = b / a
Therefore, to find the value of tan(t) for a given point (a, b) on the unit circle, you need to divide the y-coordinate by the x-coordinate: tan(t) = b / a.