Description
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
Explanation & Answer
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
Review
Review
24/7 Homework Help
Stuck on a homework question? Our verified tutors can answer all questions, from basic math to advanced rocket science!