My Math Forum  

Go Back   My Math Forum > High School Math Forum > Trigonometry

Trigonometry Trigonometry Math Forum


Thanks Tree1Thanks
  • 1 Post By mathman
Reply
 
LinkBack Thread Tools Display Modes
October 24th, 2018, 02:35 PM   #1
Newbie
 
Joined: Oct 2018
From: Indoors

Posts: 12
Thanks: 0

Identity crisis 2

((cot (x))^2+1)/sin (x) expressed in terms of cos (x) is supposedly + or - 1/(1-(cos (x))^2)^(3/2).

The graph of the left side is like a slimmer version of the csc function and not surprisingly is tangent to the minimum and maximum points of the sine function.

The graph of 1/(1-(cos (x))^2)^(3/2) is like a slimmer version of |csc (x)| function and is tangent to the maximum points of the |sin (x)| function.

The graph of -1/(1-(cos (x))^2)^(3/2) is like a slimmer version of -|csc (x)| function and is tangent to the minimum points of the -|sin (x)| function.

As you can see, these differing graphs makes me want to reevaluate identities.
TheReluctantMathMan is offline  
 
October 24th, 2018, 04:54 PM   #2
Global Moderator
 
Joined: May 2007

Posts: 6,852
Thanks: 743

What is your question?
Thanks from topsquark
mathman is offline  
October 25th, 2018, 03:00 AM   #3
Newbie
 
Joined: Oct 2018
From: Indoors

Posts: 12
Thanks: 0

If I must ask a question, it would probably have something to do with how one would reconcile the difference in these graphs considering that they are supposed to be identities. Does it not bother you that something this basic is somehow inconsistent?
TheReluctantMathMan is offline  
October 25th, 2018, 04:37 AM   #4
Global Moderator
 
Joined: Dec 2006

Posts: 21,110
Thanks: 2326

Supposed to be an identity according to what source?
skipjack is offline  
October 25th, 2018, 11:47 AM   #5
Newbie
 
Joined: Oct 2018
From: Indoors

Posts: 12
Thanks: 0

A textbook.
TheReluctantMathMan is offline  
October 25th, 2018, 01:21 PM   #6
Newbie
 
Joined: Oct 2018
From: Indoors

Posts: 12
Thanks: 0

Quote:
Originally Posted by skipjack View Post
Supposed to be an identity according to what source?
Something just dawned on me upon reading this question.
While it is true that the first expression was rewritten in terms of cos, it may not be necessarily true that they are equal or identities as indicated by their graphs.

https://www.wolframalpha.com/input/?...)%5E(3%2F2)%3F
TheReluctantMathMan is offline  
October 25th, 2018, 01:54 PM   #7
Global Moderator
 
Joined: Dec 2006

Posts: 21,110
Thanks: 2326

I wouldn't call |x| = ±x an identity. Was the textbook written by mathematics teachers?
skipjack is offline  
October 25th, 2018, 01:54 PM   #8
Global Moderator
 
Joined: May 2007

Posts: 6,852
Thanks: 743

Any expression involving square roots has to be handled carefully taking into account the two possibilities. All three expressions are (in a sense) the same, when properly handling this ambiguity.
mathman is offline  
Reply

  My Math Forum > High School Math Forum > Trigonometry

Tags
crisis, identity



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Identity crisis TheReluctantMathMan Trigonometry 1 October 23rd, 2018 08:03 AM
Octave crisis Johnnyesto Math Software 6 February 29th, 2016 07:28 AM
An identity Dacu Algebra 3 March 15th, 2014 07:45 AM
Identity. Crisis. yogazen2013 Algebra 3 September 6th, 2013 11:50 AM
identity Soha Algebra 6 December 14th, 2006 12:32 PM





Copyright © 2019 My Math Forum. All rights reserved.