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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 a finite number of maxima and minima.
- f(x) has no infinite discontinuity.
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How can arccot of tanx be simplified?
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)
How do you solve tan squared theta - tan theta equals 0?
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
Is tan squared x equal tan x squared?
Yes. Both expressions are the same.
What is the period of tan x?
The period of the function y= tan(x) is pie The periods of the functions y= cos(x) and y= sin(x) is 2pie
What angle do you need for a gradient of 1 in 20?
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)
