find sum (1 Viewer)

[Rkiuyto]

find sum

sin 1+sin 2+ sin 3+...+sin 359

 

[bored of sc]

You posted something similar to this, except it had tan's in it. Post it in the extension 2 maths forum. If I remember correctly the solution required complex numbers.

 

[Timothy.Siu]

find sum

sin 1+sin 2+ sin 3+...+sin 359

=(sin 1+sin 181)+(sin 2+182)+(sin 3+sin 183)+.....+(sin 179+sin 359)+sin 180=0

lol, i dunno if thats right

 

[Trebla]

And the solution can be found on the same website lolokay quoted on the other thread...lol
Art of Problem Solving Forum
Just sub α = 1, φ = 1 and n = 358 (or their equivalent radian form)

 

[Trebla]

Actually, I just realised it's a lot easier than I thought lol
Assuming degrees:
Use the fact that sin (360 - x)° = - sin x°
=> sin (360 - x)° + sin x° = 0
sin 1° + sin 2° + sin 3° + ....... + sin 357° + sin 358° sin 359°
= (sin 1° + sin 359°) + (sin 2° + sin 358°) + (sin 3° + sin 357°) + ...... (sin 179° + sin 181°) + sin 180°
= 0

 

[clintmyster]

=(sin 1+sin 181)+(sin 2+182)+(sin 3+sin 183)+.....+(sin 179+sin 359)+sin 180=0

lol, i dunno if thats right

your final answer is i.e. = 0 but use trebla's way. I like to call it rainbow method LOL

 

[Timothy.Siu]

your final answer is i.e. = 0 but use trebla's way. I like to call it rainbow method LOL

its the same as his method....
sin (180+x)=-sin x

 

[clintmyster]

its the same as his method....
sin (180+x)=-sin x

oh yeah it is, my bad.

 

[Rkiuyto]

nice thanks