tan(x)
sec^2x
The tangent function (tan x) is one of the three primary trigonometric functions (along with sine and cosine). It is defined as the ratio of the opposite side of a right triangle to the adjacent side, where x is the measure of one of the acute angles.
The formula for tan x is:
tan x = opposite / adjacent
For example, if you have a right triangle with a measure of 30 degrees for one of the acute angles, and the opposite side is 5 and the adjacent side is 3, then the tangent of 30 degrees is:
tan 30 = opposite / adjacent
tan 30 = 5 / 3
tan 30 = 1.6666666667 (rounded to 10 decimal places)
The value of tan x varies depending on the angle x. You can use a calculator or a table of trigonometric values to find the tangent of any given angle.
It is important to remember that the tangent function is undefined for certain angles, specifically when the adjacent side is zero (since division by zero is undefined). Therefore, the tangent of 90 degrees and its multiples is undefined.
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