```Date: Jan 21, 2009 11:37 PM
Author: matt271829-news@yahoo.co.uk
Subject: Re: Proving trigonometric identities

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 inyour case) has two solutions for A in the range 0 to 2*pi (i.e. 0 to360 degrees). Call these solutions A1 and A2. While by definition cos(A1) = cos(A2), this equality is not generally true for the other trigfunctions. 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 isintended it's necessary to have further information about A, such asthe quadrant in which it lies.
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