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Topic: Proving trigonometric identities
Replies: 32   Last Post: Jan 27, 2009 1:59 AM

 Messages: [ Previous | Next ]
 matt271829-news@yahoo.co.uk Posts: 2,136 Registered: 1/25/05
Re: Proving trigonometric identities
Posted: Jan 21, 2009 11:37 PM

On Jan 22, 3:32 am, Albert <albert.xtheunkno...@gmail.com> wrote:
> Moving away just a little away from proof of trigonometric identities
> and onto solving 'simple' trigonometric equations:
>
> When I get questions like:
> Find solutions in the range 0 degrees <= x <= 360 degrees for these
> trigonemetric equations:
> (a) sin x = 1/2;
> (b) ...
> ...
>
> Do I figure out one answer (say 30 degrees) and then think: there
> might be another answer and if so, the sin of it better be positive as
> well, which would mean it'd be in the 2nd quadrant and figure out 150
> degrees? Is that the way to do these problems because I don't have any
> worked examples whatsoever.
>
> I don't have any worked examples for questions like these either:
> (a) Write sin(theta) and tan(theta) in terms of cos(theta) when theta
> is in the first quadrant
> (b) If cosA = 9 / 41, and A is in the first quadrant, find tanA and
> cosecA.
>
> I know that you can get a calculator and solve for A using inverse
> cosine immediately, but what is the real intention of this question?
> The trig identity tan(theta) = sin(theta) / cos(theta) can be re-
> arranged for finding a value for sin(theta) but i) what is the
> significance of which quadrant theta is in (and) how do I find tanA in
> part b?

In general, the equation cos(A) = k for some known k (such as 9/41 in
your case) has two solutions for A in the range 0 to 2*pi (i.e. 0 to
360 degrees). Call these solutions A1 and A2. While by definition cos
(A1) = cos(A2), this equality is not generally true for the other trig
functions. For example, it's not generally the case that tan(A1) = tan
(A2) (in fact, tan(A1) = -tan(A2)). So, if you only know that cos(A) =
k, then tan(A), for example, is ambiguous. To know which value is
intended it's necessary to have further information about A, such as
the quadrant in which it lies.

Date Subject Author
1/20/09 Albert
1/20/09 Angus Rodgers
1/20/09 Albert
1/20/09 Angus Rodgers
1/20/09 Albert
1/20/09 Angus Rodgers
1/20/09 Angus Rodgers
1/20/09 Guest
1/20/09 Angus Rodgers
1/20/09 Albert
1/20/09 Angus Rodgers
1/20/09 matt271829-news@yahoo.co.uk
1/21/09 Albert
1/21/09 matt271829-news@yahoo.co.uk
1/23/09 Albert
1/23/09 Angus Rodgers
1/23/09 Angus Rodgers
1/23/09 Passerby
1/23/09 Dave Dodson
1/24/09 Albert
1/24/09 Angus Rodgers
1/24/09 Albert
1/26/09 Albert
1/26/09 Driveby
1/26/09 Albert
1/26/09 A N Niel
1/27/09 Albert