Nature of $y=\cos(e^{-x})$

Can anyone explain me the nature of the graph of $y=\cos(e^{-x})$ ?

You can tell me why this graph behaves in such a way, how to calculate it's period, why the period is becoming infinite when $x$ approaches $-\infty$ , etc.

In other words, tell me everything you can know about the properties of the graph.

#Geometry

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.

Markdown	Appears as
`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
- bulleted - list	bulleted list
1. numbered 2. list	numbered 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"

Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

Sort by:

Top Newest

@Calvin Lin , @Mark Hennings , @Chew-Seong Cheong , @Pi Han Goh

Vilakshan Gupta - 2 years, 4 months ago

It's obvious that there's no period.

Pi Han Goh - 2 years, 4 months ago

Okay, there's no period, but can you tell me why is the graph becoming compact, when $x$ becomes more negative?

Vilakshan Gupta - 2 years, 4 months ago

@Vilakshan Gupta – I want that, if we are not given the graph , how and what conditions we need to find to draw the graph by hand?

Vilakshan Gupta - 2 years, 4 months ago

@Vilakshan Gupta – Hint: See this relevant answer.

Pi Han Goh - 2 years, 4 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Nature of y=cos⁡(e−x)y=\cos(e^{-x})y=cos(e−x)

Comments

Nature of $y=\cos(e^{-x})$