Use the Law of Sines and the Cofunction Identities

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Use the Law of Sines and the cofunction identities to derive the following formulas from right-triangle trigonometry.

(a) sin A = opp/hyp

(b) cos A = adj/hyp

(c) tan A = opp/adj

Oct 22nd, 2017

First, those are usually the definitions of sin, cos and tan.... 

But... opp is the length of the side opposite A, and hyp is the length of the side opposite the right angle 
so... 
opp/sin(A) = hyp/sin(90) 
since sin(90) = 1 
sin(A) = opp/hyp 

cos(A) = sin(90 - A) 
adj is the side opposite the angle (90 - A) 
so cos(A) = adj/hyp ... based on the previous result 
tan(A) = sin(A)/cos(a) = (opp/hyp)/(adj/hyp) from the previous results 
==> tan(A) = opp/adj * hyp/hyp = opp/adj

Best of Luck

Jun 1st, 2015

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