tan ๐
The tangent function, usually denoted as tan ๐, is a trigonometric function that relates the opposite side of a right triangle to the adjacent side.
The tangent function, usually denoted as tan ๐, is a trigonometric function that relates the opposite side of a right triangle to the adjacent side.
To understand the tangent function, let’s consider a right triangle ABC, where angle ๐ is one of the acute angles. In this case, the adjacent side would be the side AB, and the opposite side would be the side BC.
The definition of tangent is given by the formula:
tan ๐ = opposite side / adjacent side = BC / AB
Alternatively, in terms of the lengths of the sides of the triangle:
tan ๐ = (length of BC) / (length of AB)
It’s important to note that the tangent function is only defined for acute angles in a right triangle, meaning angles that measure less than 90 degrees.
However, in mathematics, we also extend the definition of the tangent function beyond right triangles by using the unit circle. The unit circle is a circle with a radius of 1 centered at the origin of a coordinate plane.
In this case, if we draw a line segment from the origin to any point on the unit circle and create a right triangle with that line segment as the hypotenuse, the tangent of the angle formed by the line segment and the positive x-axis is equal to the y-coordinate of the point on the unit circle.
So, if we have a point (x, y) on the unit circle, the tangent of the angle formed by the positive x-axis and the line created by joining the origin and the point is given by:
tan ๐ = y-coordinate of the point / x-coordinate of the point = y / x
This extended definition of the tangent function allows us to find the tangent of any angle in the coordinate plane, not just acute angles in right triangles.
I hope this explanation helps you understand the tangent function. Let me know if you have any further questions!
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