Cosine of Angles 120, 60, 30 - Math Solution

[Terry Coates]

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

 

[berkeman]

Homework Statement:: Is there a set of three, rational, positive angles, totaling 180

120, 60,30

?

 

[SammyS]

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 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.

I assume you are looking to measure the angles in degrees.

Never mind angles adding to 180°.
What values of θ give a rational value for cos(θ), when 0° < θ ≤ 180° ?

 

[kuruman]

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?

 

[Mayhem]

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?

"A rational angle is a rational multiple of $\pi$".

Using that definition, it is a rational angle as $\frac{\pi}{3} = \frac{1}{3} \pi$ and $1/3$ is definitely rational. $\frac{\pi}{3}$ isn't rational though.