In a right angled triangle, the tan of an angle is the ratio of the lengths of the opposite side to the adjacent side.
More generally, on a coordinate plane, draw a circle with its centre at the origin and radius = 1. Draw a line at the required angle from the x-axis, measured in an anticlockwise direction. Suppose this line meets the unit circle at the point whose coordinates are (a,b). Then the tan of the angle is b/a. Make sure that both a and b have their appropriate signs.
An analytical definitions of tan(x), where x is an angle measured in radians does exist but it is rather complicated - and limitations of this browser make it even more difficult to explain. However, using the identity
tan(x) = sin(x) /cos(x)
tan(x) can be derived as the ratio of sine and cosine, where these are defined as the following infinite sums:
sin(x) = x/1! - x3/3! + x5/5! - x7/7! + ...
and
cos(x) = 1 - x2/2! + x4/4! - x6/6! + ...
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opposite/ adjacent
Tangent
Oh, dude, you're talking about trigonometry now! The ratio of the length of the opposite leg to the length of the adjacent leg in a right triangle is called the tangent of the angle. It's calculated by dividing the length of the opposite side by the length of the adjacent side. So, like, if you're trying to find that ratio, just remember to divide and conquer!
It is a function which maps the tangent ratio - any real value - to an angle in the range (-pi/2, pi/2) radians. Or (-90, 90) degrees.If tan(x) = y then x is the inverse tangent of y.It is also known as "arc tangent", and spreadsheets, such as Excel, use "atan" for this function.Warning:1/tangent = cotangent is the reciprocal, NOT the inverse.
Sine Cosine Tangent Cotangent Secant Cosecant