Re: Express each of the other trigonometric functions of t in terms of sec t.
- From: Narasimham <mathma18@xxxxxxxxxxx>
- Date: Wed, 01 Aug 2007 22:05:36 -0700
On Aug 2, 8:20 am, Will H <will.herm...@xxxxxxxxx> wrote:
The math problem:
Express each of the other trigonometric functions of t in terms of sec
t.
Can this be done with csc t and sin t since they do not contain x (ie
cos t = x therefore one can determine cos t in terms of sec t because
sec t = 1/x).
Thanks for all your help.
Sketch a right angled triangle with hypotenuse x = sec(t) with side
adjacent to angle t as 1. Then by Pythagoras, opposite side is
sqrt(x^2-1).Now just read off any trig relation you want from this
diagram.
Please understand that making of this diagram and labeling the 3 sides
in terms of the given trig function [1,x and sqrt(x^2-1) in the above
example] is essential or useful and an easy key to finding all
other required trig.functions e.g., as given in:
http://en.wikipedia.org/wiki/Trigonometric_identity#Basic_relationships
There is an ambiguity in sign of sqrt that can be fixed by considering
angle
placed in which quadrant,in the usual way.(All Silver Tea Cups).
Cheers,
Narasimham
.
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