The discussion focuses on the cosine values of angles 120°, 60°, and 30°, specifically noting that cos(120°) = -0.5, cos(60°) = 0.5, and cos(30°) = 0.866. Participants explore the concept of rational angles, concluding that while angles can be expressed as rational multiples of π, the cosine values themselves are not necessarily rational. The conversation emphasizes the need to clarify definitions of rational angles and their cosine values, particularly in the context of angles summing to 180° without including 90°.
PREREQUISITESStudents studying trigonometry, mathematics educators, and anyone interested in the properties of angles and their cosine values.
Terry Coates said:Homework Statement:: Is there a set of three, rational, positive angles, totaling 180
?Terry Coates said:120, 60,30
A little bit of thought should lead you to the answer. By the way, your Relevant Equation is not relevant. You're not necessarily looking for cosine to be an integer.Terry Coates said:Homework Statement:: Is there a set of three, rational, positive angles, totaling 180 and excluding 90 degrees such that all three have rational cosines?
Relevant Equations:: int(cos(A))= cos(A)
120, 60,30 cos 120 = -0.5, cos 60 = 0.5, cos 30 = 0.866
"A rational angle is a rational multiple of ##\pi##".kuruman said:Is rational to assume that something like ##60^o = \dfrac{\pi}{3}## is a rational angle even though it is equal to the ratio of an irrational number and an integer?