Secant, Cosecant, and Cotangent Uses
Date: Winter 2011-2012
What is the point of inverse trigonometric functions such as the secant, cosecant, and cotangent. Do they indicate negative angles in the unit circle or something?
All the trig functions can denote ratios of coordinates of points involved in the unit circle. Being ratios, they all have reciprocals. The ratios you mention are the reciprocals of other ratios. But every trig ratio is the reciprocal of another ratio. In that sense, the ratios you mention are not special in any way. Like the more familiar sin and cosine, the sec, csc and cot can be useful or not in any given problem. In calculus, you will all the ratios (and their inverses) very useful.
No, they are the original functions upside down.
In the days before calculators we used to look up values for these things in tables. A table for the inverse of sine allowed us to always multiply which was considerably easier.
Also the answers to some actual physical problems fit the inverse functions better than the original ones! Their equations are best written using the inverse functions
Hope this helps.
R. W. "Mr. A." Avakian
Oklahoma State Univ. Inst. of Technology
The "point" of inverse trigonometric functions is to provide an
answer to the question(s): "If the trig function of an angle "x" is: trig(x)
= y, then what angle, x, has the value of x = invtrig(y), that is, the
inverse trig functions "unscrew" the trig functions. It answers the question
what angle, x, has the trig function, y. You can find many discussions of
inverse trig functions by searching the term: "inverse trigonometric
functions". For example:
Inverse trigonometric functions, like the right-side-up trigonometric
functions, are used to solve triangles.
Tangent = length of side opposite the angle divided by the length of the
side adjacent to the angle.
CoTangent is equal to the inverse of the Tangent
So if the Tangent is useful, so is the Cotangent.
Here is a brief tutorial on the trigonometric functions:
Cosine, CoSecant, and CoTangent do not necessarily represent negative angles
in the unit circles.
There is a discussion of the CoSine, CoSecant, and CoTangent functions in
the unit circle in this article.
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Update: June 2012