My Math Forum  

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

Trigonometry Trigonometry Math Forum


Reply
 
LinkBack Thread Tools Display Modes
November 21st, 2017, 06:03 PM   #1
Newbie
 
Joined: Nov 2017
From: uk

Posts: 3
Thanks: 0

I don't understand the use of these trig functions for a force vector

Hi

I am trying to learn mechanics with static particles.

I have a vector that points up and left with an angle theta with respect to the vertical axis.

The answer sheet says that the direction is therefore:

V = −|V| sinθi + |V| cosθj

But I don't see how it's a negative sin trig for i component and positive cos trig for j component.

I can understand it more like:

V = |V|cos(θ+90)i + |V|sin(θ+90)j

I was hoping some one could explain how they got their answer ?

Last edited by skipjack; November 22nd, 2017 at 01:36 PM.
thefollower is offline  
 
November 21st, 2017, 06:25 PM   #2
Math Team
 
Joined: Jul 2011
From: Texas

Posts: 2,756
Thanks: 1407

x component in the negative direction

y component in the positive direction

see diagram ...
Attached Images
File Type: jpg vector_quadII.jpg (16.6 KB, 25 views)
skeeter is offline  
November 21st, 2017, 06:32 PM   #3
Newbie
 
Joined: Nov 2017
From: uk

Posts: 3
Thanks: 0

Thank you for the reply.

I've not seen it done like that before. We have only been taught doing it like this so far:



Are there other ways to visualise it without thinking about changing the i and j axis signs?

It's still not 100% obvious to me why the vertical j in your picture is using "cos" and the horizontal negative i is "sin" ? I would naturally had used "-cos" for i and "sin" for j in that image.
thefollower is offline  
November 21st, 2017, 06:55 PM   #4
Math Team
 
Joined: Jul 2011
From: Texas

Posts: 2,756
Thanks: 1407

Look at the position of $\theta$ in the right triangle ...



... the horizontal component is opposite to $\theta$ and the vertical component adjacent.

Remember SOHCAHTOA?

Last edited by skipjack; November 22nd, 2017 at 01:34 PM.
skeeter is offline  
November 21st, 2017, 06:58 PM   #5
Newbie
 
Joined: Nov 2017
From: uk

Posts: 3
Thanks: 0

Ohhhh, I see it now! It's so obvious too! Thank you.

Last edited by skipjack; November 22nd, 2017 at 01:33 PM.
thefollower is offline  
November 27th, 2017, 06:15 AM   #6
Math Team
 
Joined: Jan 2015
From: Alabama

Posts: 3,236
Thanks: 884

Since in the xi+ yj form, the angle is typically measured from the positive x-axis, you can also write that as $\displaystyle cos(\theta+ \pi/2)i+ sin(\theta+ \pi/2)j$. But $\displaystyle sin(\theta+ \phi)= sin(\theta)cos(\phi)+ cos(\theta)sin(\phi)$ and $\displaystyle cos(\theta+ \phi)= cos(\theta)cos(\phi)- sin(\theta)cos(\phi)$

So $\displaystyle sin(\theta+ \pi/2)= sin(\theta)cos(\pi/2)+ cos(\theta)sin(\pi/2)= sin(\theta)(0)+ cos(\theta)(1)= cos(\theta)$ and $\displaystyle cos(\theta+ \pi/2)= cos(\theta)(cos(\pi/2)- sin(\theta)sin(\pi/2)= cos(\theta)(0)- sin(\theta)(1)= -sin(\theta)$.

$\displaystyle cos(\theta+ \pi/2)i + sin(\theta+ \pi/2)j= -sin(\theta)i + cos(\theta)j$.
Country Boy is offline  
Reply

  My Math Forum > High School Math Forum > Trigonometry

Tags
force, functions, trig, understand, vector



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
(Vector)How to find the force? williamwong0402 Geometry 3 December 11th, 2016 10:36 PM
Working out piston force using trig eddm87 Trigonometry 3 October 3rd, 2016 03:45 AM
Help: Trig w/ Force Vectors Application TaylorM0192 Algebra 1 September 13th, 2009 06:24 PM
Vector force field help please!! yoyosuper8 Calculus 6 April 26th, 2009 08:26 PM
I can't understand some functions Creephun Real Analysis 0 December 31st, 1969 04:00 PM





Copyright © 2018 My Math Forum. All rights reserved.