## pythagoren identities: cosec Theta = a, give other ratios

Trigonometric ratios and functions, the unit circle, inverse trig functions, identities, trig graphs, etc.
ianhendry
Posts: 4
Joined: Wed Feb 01, 2012 2:06 am
Contact:

### pythagoren identities: cosec Theta = a, give other ratios

I have a question that i am finding a different answer then one given. pleas explain where i am going wrong.
given: cosec Theta = a so i know sin = 1/a

cos = sqrt (1-(1/a)^2)
how do they come up with sqrt (a^2-1)/a

i left school too early 22 years ago. college algebra wasn't so bad but this is turning my mind to mush, mental block.

Hope someone can explain this for me. and ill find the reciprocals etc through that.

stapel_eliz
Posts: 1733
Joined: Mon Dec 08, 2008 4:22 pm
Contact:
ianhendry wrote:cos = sqrt (1-(1/a)^2)
how do they come up with sqrt (a^2-1)/a

Simplify (1/a)2. Convert 1 - (the simplified result) to a common denominator. Take the square root. What do you get?

ianhendry
Posts: 4
Joined: Wed Feb 01, 2012 2:06 am
Contact:

### Re: pythagoren identities: cosec Theta = a, give other ratio

hmm i see sqrt(1-1) 1/1 *a/a the a going back under the root gets ^2 theirfore sqrt (a^2 -1)....over a+a Denominators = a... simple fraction rules. i over thought that.

Thanks a 1000^2

stapel_eliz
Posts: 1733
Joined: Mon Dec 08, 2008 4:22 pm
Contact:

### Re: pythagoren identities: cosec Theta = a, give other ratio

ianhendry wrote:hmm i see sqrt(1-1) 1/1 *a/a the a going back under the root gets ^2 theirfore sqrt (a^2 -1)

I'm sorry, but I don't understand what you mean...?

What did you get when you simplified (1/a)2?

What did you get when you subtracted the result from 1, starting with converting the 1 = 1/1 to the common denominator?

What did you get when you split the square root of a fraction into a fraction made with two square roots, and then simplified the denominator?

ianhendry
Posts: 4
Joined: Wed Feb 01, 2012 2:06 am
Contact:

### Re: pythagoren identities: cosec Theta = a, give other ratio

{{{ sqrt (1-1/a^2) }}}
sqrt1-1/1-a
a/a*1/1=a/a
sqrt (a^2-1)/a

stapel_eliz
Posts: 1733
Joined: Mon Dec 08, 2008 4:22 pm
Contact:
ianhendry wrote:{{{ sqrt (1-1/a^2) }}}
sqrt1-1/1-a

How did:

. . . . .$1\, -\, \frac{1}{a^2}$

...become:

. . . . .$1\,-\, \frac{1}{1\, -\, a}$

Instead, try following the steps provided earlier, starting with converting to a common denominator (in this case, $a^2$ would be the denominator) and then combining the two fractions.