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leonhard euler
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∙ 12y ago
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Can e be expressed in terms of sine and cosine?
the only close answer i know is: eix = cos(x)+i*sin(x) where i is imaginary unit
What is the population of Eix?
The population of Eix is 223.
What are five trigonometric identities?
All others can be derived from these and a little calculus: sin2x+cos2x=1 sec2x-tan2x=1 sin(a+b)=sin(a)cos(b)+sin(b)sin(a) cos(a+b)=cos(a)cos(b)-sin(a)sin(b) eix=cos(x)+i*sin(x)
What is the area of Eix?
The area of Eix is 12.06 square kilometers.
How do you solve double angle equations for trigonometry?
There are two ways to solve for the double angle formulas in trigonometry. The first is to use the angle addition formulas for sine and cosine. * sin(a + b) = sin(a)cos(b) + cos(a)sin(b) * cos(a + b) = cos(a)cos(b) - sin(a)sin(b) if a = b, then * sin(2a) = sin(a)cos(a) + cos(a)sin(a) = 2sin(a)cos(a) * cos(2a) = cos2(a) - sin2(b) The cooler way to solve for the double angle formulas is to use Euler's identity. eix = cos(x) + i*sin(x). Yes, that is "i" as in imaginary number. we we put 2x in for x, we get * e2ix = cos(2x) + i*sin(2x) This is the same as * (eix)2 = cos(2x) + i*sin(2x) We can substitute our original equation back in for eix. * (cos(x) + i*sin(x))2 = cos(2x) + i*sin(2x) We can distribute the squared term. * cos2(x) + i*sin(x)cos(x) + i*sin(x)cos(x) + (i*sin(x))2 = cos(2x) + i*sin(2x) And simplify. Because i is SQRT(-1), the i squared term becomes negative. * cos2(x) + 2i*sin(x)cos(x) - sin2(x) = cos(2x) + i*sin(2x) * cos2(x) - sin2(x) + 2i*sin(x)cos(x) = cos(2x) + i*sin(2x) Now you can plainly see both formulas in the equation arranged quite nicely. I don't yet know how to get rid of the i, but I'm working on it.
What is the market cap for Edison International EIX?
As of July 2014, the market cap for Edison International (EIX) is $18,558,206,293.76.
What is Leonard Euler's famous formula?
eix = cos(x) + i*sin(x) where e is the irrational number 2.7182... i is the maginary sq root of -1 and x is measured in radians. In the special case when x = pi, this reduces to: eiπ = cos(π) + i*sin(π) or eiπ = -1
How do you derive sin2x?
If you are refering to the double-angle formula for sin(x), the best way is to use what is known as Euler's identity. Euler's identity is eix = cos(x) + i*sin(x) where x is any real angle in radians, e is Euler's constant 2.71828182845... and i is the imaginary number: SQRT(-1). Assuming that is true, then ei(2x) = cos(2x) + i*sin(2x) and that is the same as saying (eix)2= cos(2x) + i*sin(2x) and substituting from the original equation: (cos(x) + i*sin(x))2 = cos(2x) + i*sin(2x). By distribution, remembering that i2 = -1, we get cos2(x) + i*2*sin(x)*cos(x) - sin2(x) = cos(2x) + i*sin(2x). Now we can separate the equation into its real and imaginary parts. cos2(x) - sin2(x) = cos(2x) and i*2*sin(x)*cos(x) = i*sin(2x), and after i cancels, there's our good old double angle formula. If derive refers to derivative, then use the chain rule. d(sin(2x))/dx=2cos(2x)
What is euler's formula?
Euler's formula states that, for any real number x,eix = cos x + i sin xwhere e is the base of the natural logarithm, i is the imaginary unit, and cos and sin are the trigonometric functions cosine and sine respectively, with the argument x given in radians.[Sources:][1] My own knowledge.[2] linked
What does Euler's formula equal?
Euler's formula states that, for any real number x,eix = cos x + i sin x,where e is the base of the natural logarithm, i is the imaginary unit, and cos and sin are the trigonometric functions cosine and sine, respectively. The argument x is given in radians.Please see the related link below for more information.
What is the symbol for Edison International in the NYSE?
The symbol for Edison International in the NYSE is: EIX.
What is the formula for Euler?
Euler's formula states that: eix = cos(x) + i*sin(x); where "i" is an imaginary number and "x" is an angle value. Under this reasoning, ei*2(pi) equals 1: ei*2(pi) = cos(2(pi)) + i*sin(2(pi)); ei*2(pi) = 1 + i*(0); ei*2(pi) = 1 + 0; ei*2(pi) = 1. Another contributor: Equivalently, e2i*pi - 1 = 0 That statement brings together, in such simplicity, two of the most important transcendental numbers (e and pi), the basic element of complex mathematics (i) and the two identities of arithmetical operations: addition (0), and multiplication (1).
