euler's formula:TomMe said:How can I calculate cos 72° and sin 72° using complex numbers, and without the use of a calculator?
I noticed that 5*72° = 360° so (cos 72° + i*sin 72°)^5 = 1. But, I don't quite know how to go from there.. :shy:
That formula arrives at a later chapter in the book, so strictly speaken I can't use it.quetzalcoatl9 said:euler's formula:
[tex]e^{i x} = cos x + i sin x[/tex]
First know you can do this either by drawing triangles or by expanding sin(5x) and that useing complex numbers (while fun) is not needed. Your observation is the same as the fact that z^5=1 has roots whose real and imaginary parts are cosines and sines of 72°,144°,216°,288°,360°. z^5=1 is hard to solve so let z=x+y iTomMe said:How can I calculate cos 72° and sin 72° using complex numbers, and without the use of a calculator?
I noticed that 5*72° = 360° so (cos 72° + i*sin 72°)^5 = 1. But, I don't quite know how to go from there.. :shy: