Re: the code messed up message I hope this one works

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Posted by Brad Paul on September 28, 2002 at 15:16:51:

In Reply to: the code messed up message I hope this one works posted by June on September 28, 2002 at 13:51:24:

: : the question is find sin 2, cos 2, tan 2.
: : tan x = -sqrt 2 and pi/2 < x < pi
: : How do you find cos and sin when you just know tan, I can't find any examples in the book.

I'm not real sure what the full question is here so I will answer the
following question:

How do you find cos and sin when you just know tan? Or any combination.

Let's say you have :

cos(t)=v and you want sin(t) and/or tan(t) etc.

You know that if you had a right triangle the cos of one of the corner
angles is cos(angle)=(closest leg)/(hypotenuse). Well I can write

cos(t)=v=v/1

Now if I draw a right triangle I can label the hypotenuse with a length
of 1 and the closest side as length v. I can then find the length of
the last unlabeled side to be sqrt(1-v2). Now that I have a
fully labeled right triangle I can find all the trig functions of the
angle t

sin(t)=(far side)/(hypotenuse)=sqrt(1-v2)/1=sqrt(1-v2)

tan(t)=(far side)/(closest leg)=sqrt(1-v2)/v

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