y=tanx cannot be expressed as a Fourier series, since it has infinite number of infinite discontinuity.
Dirichlet’s condition or the sufficient condition for a function f(x) to be expressed as a Fourier series.
- f(x) is single valued, finite and periodic.
- f(x) has a finite number of finite discontinuities.
- f(x) has no infinite discontinuity.
There is not much that can be done by way of simplification. Suppose arccot(y) = tan(x) then y = cot[tan(x)] = 1/tan(tan(x)) Now cot is NOT the inverse of tan, but its reciprocal. So the expression in the first of above equation cannot be simplified further. Similarly tan[tan(x)] is NOT tan(x)*tan(x) = tan2(x)
Let x = theta, since it's easier to type, and is essentially the same variable. Since tan^2(x)=tan(x), you know that tan(x) must either be 1 or zero for this statement to be true. So let tan(x)=0, and solve on your calculator by taking the inverse. Similarly for, tan(x)=1
Yes. Both expressions are the same.
The period of the function y= tan(x) is pie The periods of the functions y= cos(x) and y= sin(x) is 2pie
If the angle is x radians, then tan(x) = 1/20 = 0.05 So x = tan-1(0.05) = 0.04996 radians = 2.86 degrees (approx)
half range--- 0 to x full range--- -x to x
x
1 (sec x)(sin x /tan x = (1/cos x)(sin x)/tan x = (sin x/cos x)/tan x) = tan x/tan x = 1
cot2x-tan2x=(cot x -tan x)(cot x + tan x) =0 so either cot x - tan x = 0 or cot x + tan x =0 1) cot x = tan x => 1 / tan x = tan x => tan2x = 1 => tan x = 1 ou tan x = -1 x = pi/4 or x = -pi /4 2) cot x + tan x =0 => 1 / tan x = -tan x => tan2x = -1 if you know about complex number then infinity is the solution to this equation, if not there's no solution in real numbers.
tan(-x) = -tan(x)
The Fourier transform of the function f(x) 1/r is 1/k, where k is the wave number.
No. Tan(x)=Sin(x)/Cos(x) Sin(x)Tan(x)=Sin2(x)/Cos(x) Cos(x)Tan(x)=Sin(x)
There is not much that can be done by way of simplification. Suppose arccot(y) = tan(x) then y = cot[tan(x)] = 1/tan(tan(x)) Now cot is NOT the inverse of tan, but its reciprocal. So the expression in the first of above equation cannot be simplified further. Similarly tan[tan(x)] is NOT tan(x)*tan(x) = tan2(x)
tan x
tan(x)*csc(x) = sec(x)
The definition of tan(x) = sin(x)/cos(x). By this property, cos(x)tan(x) = sin(x).
tanx = 2*(sin2x - sin4x + sin6x - ... )However, be warned that this series is very slow to converge.