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  • Identical expressions

  • log(tan((ninety +x)*pi/ three hundred and sixty))/(pi/ one hundred and eighty)
  • logarithm of ( tangent of ((90 plus x) multiply by Pi divide by 360)) divide by ( Pi divide by 180)
  • logarithm of ( tangent of ((ninety plus x) multiply by Pi divide by three hundred and sixty)) divide by ( Pi divide by one hundred and eighty)
  • log(tan((90+x)pi/360))/(pi/180)
  • logtan90+xpi/360/pi/180
  • log(tan((90+x)*pi divide by 360)) divide by (pi divide by 180)

  • Similar expressions

  • log(tan((90-x)*pi/360))/(pi/180)
Plotting a function graph/ log(tan((90+x)*pi/360))/(pi/180)

Graphing y = log(tan((90+x)*pi/360))/(pi/180)

v

The graph:

from to

Intersection points:

does show?

Piecewise:

The solution

You have entered [src] 
          /   /(90 + x)*pi\\
       log|tan|-----------||
          \   \    360    //
f(x) = ---------------------
               / pi\        
               |---|        
               \180/
$$f{\left(x \right)} = \frac{\log{\left(\tan{\left(\frac{\pi \left(x + 90\right)}{360} \right)} \right)}}{\frac{1}{180} \pi}$$ 
f = log(tan((pi*(x + 90))/360))/((pi/180))
The graph of the function
The points of intersection with the Y axis coordinate
The graph crosses Y axis when x equals 0:
substitute x = 0 to log(tan(((90 + x)*pi)/360))/((pi/180)).
$$\frac{\log{\left(\tan{\left(\frac{90 \pi}{360} \right)} \right)}}{\frac{1}{180} \pi}$$
The result:
$$f{\left(0 \right)} = 0$$
The point:
(0, 0)
Extrema of the function
In order to find the extrema, we need to solve the equation
$$\frac{d}{d x} f{\left(x \right)} = 0$$
(the derivative equals zero),
and the roots of this equation are the extrema of this function:
$$\frac{d}{d x} f{\left(x \right)} = $$
the first derivative
$$\frac{\frac{180}{\pi} \pi \left(\tan^{2}{\left(\frac{\pi \left(x + 90\right)}{360} \right)} + 1\right)}{360 \tan{\left(\frac{\pi \left(x + 90\right)}{360} \right)}} = 0$$
Solve this equation
Solutions are not found,
function may have no extrema
Inflection points
Let's find the inflection points, we'll need to solve the equation for this
$$\frac{d^{2}}{d x^{2}} f{\left(x \right)} = 0$$
(the second derivative equals zero),
the roots of this equation will be the inflection points for the specified function graph:
$$\frac{d^{2}}{d x^{2}} f{\left(x \right)} = $$
the second derivative
$$- \frac{\pi \left(\frac{\tan^{2}{\left(\pi \left(\frac{x}{360} + \frac{1}{4}\right) \right)} + 1}{\tan^{2}{\left(\pi \left(\frac{x}{360} + \frac{1}{4}\right) \right)}} - 2\right) \left(\tan^{2}{\left(\pi \left(\frac{x}{360} + \frac{1}{4}\right) \right)} + 1\right)}{720} = 0$$
Solve this equation
The roots of this equation
$$x_{1} = -180$$
$$x_{2} = 0$$

Сonvexity and concavity intervals:
Let’s find the intervals where the function is convex or concave, for this look at the behaviour of the function at the inflection points:
Concave at the intervals
$$\left(-\infty, -180\right] \cup \left[0, \infty\right)$$
Convex at the intervals
$$\left[-180, 0\right]$$
Horizontal asymptotes
Let’s find horizontal asymptotes with help of the limits of this function at x->+oo and x->-oo
True

Let's take the limit
so,
equation of the horizontal asymptote on the left:
$$y = \lim_{x \to -\infty}\left(\frac{\log{\left(\tan{\left(\frac{\pi \left(x + 90\right)}{360} \right)} \right)}}{\frac{1}{180} \pi}\right)$$
True

Let's take the limit
so,
equation of the horizontal asymptote on the right:
$$y = \lim_{x \to \infty}\left(\frac{\log{\left(\tan{\left(\frac{\pi \left(x + 90\right)}{360} \right)} \right)}}{\frac{1}{180} \pi}\right)$$
Inclined asymptotes
Inclined asymptote can be found by calculating the limit of log(tan(((90 + x)*pi)/360))/((pi/180)), divided by x at x->+oo and x ->-oo
True

Let's take the limit
so,
inclined asymptote equation on the left:
$$y = x \lim_{x \to -\infty}\left(\frac{\frac{180}{\pi} \log{\left(\tan{\left(\frac{\pi \left(x + 90\right)}{360} \right)} \right)}}{x}\right)$$
True

Let's take the limit
so,
inclined asymptote equation on the right:
$$y = x \lim_{x \to \infty}\left(\frac{\frac{180}{\pi} \log{\left(\tan{\left(\frac{\pi \left(x + 90\right)}{360} \right)} \right)}}{x}\right)$$
Even and odd functions
Let's check, whether the function even or odd by using relations f = f(-x) и f = -f(-x).
So, check:
$$\frac{\log{\left(\tan{\left(\frac{\pi \left(x + 90\right)}{360} \right)} \right)}}{\frac{1}{180} \pi} = \frac{180}{\pi} \log{\left(\tan{\left(\pi \left(\frac{1}{4} - \frac{x}{360}\right) \right)} \right)}$$
- No
$$\frac{\log{\left(\tan{\left(\frac{\pi \left(x + 90\right)}{360} \right)} \right)}}{\frac{1}{180} \pi} = - \frac{180}{\pi} \log{\left(\tan{\left(\pi \left(\frac{1}{4} - \frac{x}{360}\right) \right)} \right)}$$
- No
so, the function
not is
neither even, nor odd
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