My Math Forum  

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

Trigonometry Trigonometry Math Forum


Thanks Tree3Thanks
Reply
 
LinkBack Thread Tools Display Modes
January 11th, 2019, 05:56 PM   #11
Global Moderator
 
Joined: Dec 2006

Posts: 20,972
Thanks: 2222

The inequalities $a+b>c,\, a+c>b,\, b+c>a$ are known as the triangle inequality.

Your third and fourth identities can be written as

$(c\times\sin B)^2+(c\times\cos B)^2=c^2$
and
$(c\times\sin A)^2+(c\times\cos A)^2=c^2$

so that they hold for any value of $c$, not just when $c$ is 1. Hence my change to this effect in your previous list.

As $c\times\sin B = b\times\sin C$,
$(c\times\sin B)^2+(b\times\cos C)^2=b^2$ is equivalent to $(b\times\sin C)^2+(b\times\cos C)^2=b^2$,
which can be simplified to $\sin^2\! C + \cos^2\! C = 1$.

I think all the identities you listed can be found on Wikipedia.
Thanks from topsquark
skipjack is online now  
 
January 13th, 2019, 09:52 AM   #12
Newbie
 
Joined: Jan 2018
From: Ontario

Posts: 11
Thanks: 0

Correction for the fourth line.

$(b\times\cos A)^2+(a\times\cos B)^2=c^2$
Larrousse is offline  
January 13th, 2019, 01:15 PM   #13
Newbie
 
Joined: Jan 2018
From: Ontario

Posts: 11
Thanks: 0

For side c so the base is not only 1the equations are:

$(c\times\sin B)^2+(c\times\cos B)^2=c^2$

$(c\times\sin A)^2+(c\times\cos A)^2=c^2$
Larrousse is offline  
January 13th, 2019, 01:17 PM   #14
Newbie
 
Joined: Jan 2018
From: Ontario

Posts: 11
Thanks: 0

Quote:
Originally Posted by skipjack View Post
The inequalities $a+b>c,\, a+c>b,\, b+c>a$ are known as the triangle inequality.

Your third and fourth identities can be written as

$(c\times\sin B)^2+(c\times\cos B)^2=c^2$
and
$(c\times\sin A)^2+(c\times\cos A)^2=c^2$

so that they hold for any value of $c$, not just when $c$ is 1. Hence my change to this effect in your previous list.

As $c\times\sin B = b\times\sin C$,
$(c\times\sin B)^2+(b\times\cos C)^2=b^2$ is equivalent to $(b\times\sin C)^2+(b\times\cos C)^2=b^2$,
which can be simplified to $\sin^2\! C + \cos^2\! C = 1$.

I think all the identities you listed can be found on Wikipedia.
Thanks
Larrousse is offline  
January 13th, 2019, 06:50 PM   #15
Math Team
 
Joined: Oct 2011
From: Ottawa Ontario, Canada

Posts: 14,597
Thanks: 1038

Regarde dans le dictionnaire Larousse
Denis is offline  
January 13th, 2019, 09:52 PM   #16
Global Moderator
 
Joined: Dec 2006

Posts: 20,972
Thanks: 2222

Quote:
Originally Posted by Larrousse View Post
Correction for the fourth line.

$(b\times\cos A)^2+(a\times\cos B)^2=c^2$
That's incorrect. I'm not sure what you intended.
skipjack is online now  
January 14th, 2019, 12:52 AM   #17
Newbie
 
Joined: Jan 2018
From: Ontario

Posts: 11
Thanks: 0

Quote:
Originally Posted by skipjack View Post
That's incorrect. I'm not sure what you intended.
It's an error, disregard it.
Larrousse is offline  
Reply

  My Math Forum > High School Math Forum > Trigonometry

Tags
detailed, magical, properties, section, triangles, unexplained



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Unexplained error message Carl James Mesaros Computer Science 2 April 13th, 2017 12:49 AM
Halting chance (chaitins constant) has a more detailed form related to pagerank BenFRayfield Computer Science 0 February 11th, 2015 08:06 PM
please, help me with a detailed answer qskti Linear Algebra 0 January 9th, 2015 09:57 AM
Does anyone know where to find a fully detailed solutions... jonas Algebra 1 November 12th, 2009 10:55 PM





Copyright © 2019 My Math Forum. All rights reserved.