Weirdness is in graphs!

As you all already know how the graph of f(x)=sinxxf\left(x\right)=\frac{\sin x}{x} looks like, try graphing f(x)=sin(1(x))1xf\left(x\right)=\frac{\sin \left(\frac{1}{\left(x\right)}\right)}{\frac{1}{x}}. (Yes! You're allowed to graph it using an electronic graphing calculator, or use the Desmos Graphing Calculator.)

Try graphing the following too!

tan(xcos(1x))\tan \left(\frac{x}{\cos \left(\frac{1}{x}\right)}\right)

tan(x(secx))\tan \left(\frac{x}{\left(\sec x\right)}\right). (Nothing? Zoom out for the climax!)

The bombshell:

sin(cos(tan(csc(sec(cot(arcsin(arccos(arctan(arccsc(arcsec(arccot(x)))))))))))) \sin \left(\cos \left(\tan \left(\csc \left(\sec \left(\cot \left(\arcsin \left(\arccos \left(\arctan \left(\operatorname{arccsc}\left(\operatorname{arcsec}\left(\operatorname{arccot}\left(x\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)\right)

And your device starts lagging a bit too as you move towards the negative x-axis.

exln(sin(ecos(1(((x))))))\frac{e^x}{\ln \left(\sin \left(e^{\cos \left(\frac{1}{\left(\left(\left(x\right)\right)\right)}\right)}\right)\right)}

Seems as if the curve is a fan of the negative y-axis!

sin(1e1arccsc(x))\sin \left(\frac{1}{e^{\frac{1}{\operatorname{arccsc}\left(x\right)}}}\right)

Kindly move towards the negative x-axis.

yx=sec(20x) y^x=\sec \left(20x\right)

Clearly, this time the graphing calculator gave up!

You're free to share any such function which has such a peculiar curve in the comments section. Cheers! :D

GIF Credit: Reddit

Note by Arkajyoti Banerjee
3 years, 3 months ago

No vote yet
1 vote

  Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

  • Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
  • Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
  • Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
  • Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 2×3 2 \times 3
2^{34} 234 2^{34}
a_{i-1} ai1 a_{i-1}
\frac{2}{3} 23 \frac{2}{3}
\sqrt{2} 2 \sqrt{2}
\sum_{i=1}^3 i=13 \sum_{i=1}^3
\sin \theta sinθ \sin \theta
\boxed{123} 123 \boxed{123}

Comments

Sort by:

Top Newest

Weird weird weird!!!

Athenkosi Bezana - 3 years, 3 months ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...