Prove it!

[qabawe]

Prove without using a calculater that

 

cos36 -cos72 =1/2

[Fuzzwood]

The most sentient thing i can say atm is that 72 is an angle twice as big as 36

[Klaynos]

Are you familiar with any trig identities?

[MrMongoose]

Also, are you familiar with the word please?

[Daecon]

Prove without using a calculater that

 

cos36 -cos72 =1/2

Well, because it is?

 

Going from the fact that 36 is one-half of 72, I would assume that cos25 - cos50 is also 1/2?

[gonelli]

Well, because it is?

 

Going from the fact that 36 is one-half of 72, I would assume that cos25 - cos50 is also 1/2?

 

I agree with your very valid point "because it is", but unfortunately cos25 - cos50 isn't equal to 1/2, it's closer to 0.2635

[swansont]

Trig functions are not linear.

 

The easiest way to do this is to memorize all of the values of cosine for the various fractional values of pi. Otherwise I assume it's fair game that you know that pi/6 gives 1/2, and use the angle addition and subtraction formulae.

[Daecon]

How many fractional values would that be? A couple of dozen?

 

Maybe I should study maths. It sounds easy enough, except my brain doesn't have enough RAM to handle numbers over single digits...

[Math Team]

cos(36) - cos(72) = 0.40347889260888592

[swansont]

cos(36) - cos(72) = 0.40347889260888592

 

No, it's 0.5

 

36 and 72 degrees. I don't get your answer even in radians, so I don't know where you made your mistake.

[Bignose]

How many fractional values would that be? A couple of dozen?

 

Maybe I should study maths. It sounds easy enough, except my brain doesn't have enough RAM to handle numbers over single digits...

 

Every 15 degrees has a "special" representation

 

[math]\sin(\frac{\pi}{12} = 15\deg) = \frac{\sqrt{2}}{4} (\sqrt{3}-1) = \frac{\sqrt{6}-\sqrt{2}}{4}[/math]

 

[math]\sin(\frac{\pi}{6} = 30\deg) = \frac{{1}}{2}[/math]

 

[math]\sin(\frac{\pi}{4} = 45\deg) = \frac{\sqrt{2}}{2}[/math]

 

[math]\sin(\frac{\pi}{3} = 60\deg) = \frac{\sqrt{3}}{2}[/math]

 

[math]\sin(\frac{5\pi}{12} = 75\deg) = \frac{\sqrt{2}}{4} (\sqrt{3}+1) = \frac{\sqrt{6}+\sqrt{2}}{4}[/math]

 

[math]\sin(\frac{\pi}{2} = 90\deg) = 1[/math]

[Balkazrar]

Prove without using a calculater that

 

cos36 -cos72 =1/2

 

maybe you can prove this by using logorythm tables but those are extinct i say go with what eveyone says cos72=cos2(36) but without a calculators is very much impossible for most since we have no values to work with and no idea what cos36 is.