qabawe Posted February 2, 2008 Share Posted February 2, 2008 Prove without using a calculater that cos36 -cos72 =1/2 Link to comment Share on other sites More sharing options...
Fuzzwood Posted February 2, 2008 Share Posted February 2, 2008 The most sentient thing i can say atm is that 72 is an angle twice as big as 36 Link to comment Share on other sites More sharing options...
Klaynos Posted February 2, 2008 Share Posted February 2, 2008 Are you familiar with any trig identities? Link to comment Share on other sites More sharing options...
MrMongoose Posted February 2, 2008 Share Posted February 2, 2008 Also, are you familiar with the word please? Link to comment Share on other sites More sharing options...
Daecon Posted February 3, 2008 Share Posted February 3, 2008 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? Link to comment Share on other sites More sharing options...
gonelli Posted February 3, 2008 Share Posted February 3, 2008 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 Link to comment Share on other sites More sharing options...
swansont Posted February 3, 2008 Share Posted February 3, 2008 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. Link to comment Share on other sites More sharing options...
Daecon Posted February 3, 2008 Share Posted February 3, 2008 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... Link to comment Share on other sites More sharing options...
Math Team Posted February 7, 2008 Share Posted February 7, 2008 cos(36) - cos(72) = 0.40347889260888592 Link to comment Share on other sites More sharing options...
swansont Posted February 7, 2008 Share Posted February 7, 2008 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. Link to comment Share on other sites More sharing options...
Bignose Posted February 7, 2008 Share Posted February 7, 2008 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] Link to comment Share on other sites More sharing options...
Balkazrar Posted February 11, 2008 Share Posted February 11, 2008 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. Link to comment Share on other sites More sharing options...
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