range of cos theta, sin theta, and tan theta

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defeated_soldier

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Apr 15, 2006
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Hi, i want to know the range of cos theta , sin theta and tan theta .

if i know the range of above , can i get the range of their reciprocals ?
 
y=cos@
domain : -oo<@<oo radians
range: 1<y<-1

@=cos y reciprocal
y=cos^-1 @

yes you can obtain the range of of the reciprocal.
===========================================
y=sin@
domain -oo<@<oo radians
range: -1<y<1

@=sin Y
y=sin^-1 @ reciprocal
==============================================
y=tan@
domain: -oo<@<oo
range: -oo<y<oo

@=tan y
y=tan^-1 @

Arthur
 
I made a atrocious blunder!
my answer to the reciprocal is wrong

y=cos@
is this a equation or a relationship? [Only equations have domains and ranges]
A vertical line crosses the curve only once, thus it is a equation.
domain: -oo<@<oo
range: -1<y<1

reciprocal @=cosy
y=cos^-1 @
is this a equation? no! a vertical line crosses the equation a infinite number of times[more than once]
y=cos^-1@ is a relationship

there is no domain or range for the reciprocal
=================================================
same arguments for the sin@ and tan@

Arthur
there is no
 
Re: range of angles

defeated_soldier said:
Hi, i want to know the range of cos theta , sin theta and tan theta .

if i know the range of above , can i get the range of their reciprocals ?
Click to expand...

actually my question was something different ,

i was not able to map the range with the definition.

For example , cos theta = base /hypo

and base , and hypo is always positive and also base <hypo ...so cos theta can never be >1

similarly , how can i define cos theta >-1 likewise ?



How about the cases with sin theta and tan theta ?

and by reciprocal , i wanted to mean the status of sec theta , cot theta and cosec theta.

Of course , the rages are given in book ....but i dont want to by heart the fact at the very first , i want to judge it and want to find those values (ranges)logically or scientifically.
 
I don't know what you mean by "base /hypo", etc, but the inverse fucntions (and their domains and ranges) can be determined quite logically.

Look in your book, and compare the graphs of the sine, cosine, and tangent with the graphs of their inverse functions.

To be invertible, a function has to pass the Horizontal Line Test (as you learned back in algebra). Naturally, the entire (repeating) original functions cannot be invertible. Yet we have inverses! This was accomplished by taking only portions of each of the original functions.

By comparing the graphs and thinking for a few moments, it should be fairly obvious which portion of each is logical.

Eliz.
 
y=cos @
this is a function because a vertical line crosses the curve only once.
the domain,[or possible @ values ] of @ are from minus infinity to plus infinity in radians or degrees.
you can define cos @ as adjacect over hypoteneuse in a right triangle
you can define cos@ as a series 1-@^2/2! + @^4/4! -@^6/6! +.....
you can define cos@ as the real part of e^(j@) where j is the square root of -1

there are other definitions, which one you want I do not know

to find the reciprocal replace y and @, and solve for y
@=cos y
y=cos^-1 @

this is not a function but a relationship, because a vertical line cuts the graph more than once
there is no domain or range of the reciprocal ANSWER


The identical argument holds for the sin@ and tan @

Arthur
 
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