3 ms·
So to broadcast my math ignorance to all: Why does cos(pi) + i sin(pi) == -1 ?? Why does i disappear in this? Edit: Thanks to the replies below.
by sophacles 17y ago
So to broadcast my math ignorance to all:
Why does cos(pi) + i sin(pi) == -1 ??
Why does i disappear in this?
Edit: Thanks to the replies below.
- rottencupcakes 17y agoWe verify in a quick Google search: http://www.google.com/search?hl=en&safe=off&q=sin(pi)&aq=f&oq=&aqi=g10 http://www.google.com/search?hl=en&safe=off&q=sin(pi... that sin(pi) = 0.
- deleted 17y ago[deleted]
- amalcon 17y agosin(pi)=0 I wouldn't feel ignorant or anything. The article left out that information seemingly on purpose, presumably so that people would try to figure out where the i went.
- travisjeffery 17y agoThe formula is: e^(ix) = cos(x) - i sin(x) Since sin(π) == 0, i * 0 == 0 so you have cos(π) left which is -1. So in sum: e^(i π) = cos(π) - i sin(π) == -1 - 0 == -1
- catzaa 17y agoIf you draw a Sine graph, you will see that sin(x) is zero at 0, pi, 2*pi, ... If you draw a cosine graph you will see that it is -1 at pi. Therefore in the above sum the sine part just falls away. It is easy to see that the above is true when you recall that cosine(theta) = adjacent side/(hypotenuse). Since pi=180 degrees, adjacent will be -1 hypotenuse 1 and opposite side 0.