Can Someone Explain This Trig Picture to Me?

AI Thread Summary
The discussion revolves around understanding the use of sine and cosine in the context of the dot product in trigonometry. The user is confused about the application of these functions when projecting vectors onto different axes, particularly regarding the angles involved. They correctly identify the angles between vectors but struggle with the calculations, especially the last projection involving phi and y. The confusion centers on why the result for phi dot y is stated as +cos(phi) when the diagram suggests otherwise. Clarification on these trigonometric relationships is needed for better comprehension.
Meadman23
Messages
43
Reaction score
0
Its the attached picture. I'm not seeing why when using the dot product, they start using sin.
 

Attachments

  • untitled.JPG
    untitled.JPG
    8.8 KB · Views: 456
Last edited:
Mathematics news on Phys.org
The picture is self explanatory. If you know trig, it should be elementary.
 
Projections onto different axes.
 
I'm just not getting it. '
I see that the angle between r and x is phi, thus in using the formula, r (dot) x = (1)(1) cos(phi).

Then I see the angle between r and y is (90-phi), thus in using the formula, r (dot) y = (1)(1)cos(90-phi) = sin (phi).

I then see the angle between phi and x is (90 +phi), thus in using the formula, phi (dot) x = (1)(1)cos(90+phi) = -sin (phi)

I then see the angle between phi and y is (180 - phi), thus in using the formula, phi (dot) y = (1)(1)cos(180-phi) = -cos (phi)?

I don't get why the last one is +cos(phi)...
 
Look at the blue part of the diagram ... phi(dot)y = cos(phi).
 
Thread 'Video on imaginary numbers and some queries'

Thread 'Video on imaginary numbers and some queries'

Hi, I was watching the following video. I found some points confusing. Could you please help me to understand the gaps? Thanks, in advance! Question 1: Around 4:22, the video says the following. So for those mathematicians, negative numbers didn't exist. You could subtract, that is find the difference between two positive quantities, but you couldn't have a negative answer or negative coefficients. Mathematicians were so averse to negative numbers that there was no single quadratic...
View full post »

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »
Thread 'Unit Circle Double Angle Derivations'

Thread 'Unit Circle Double Angle Derivations'

Here I made a terrible mistake of assuming this to be an equilateral triangle and set 2sinx=1 => x=pi/6. Although this did derive the double angle formulas it also led into a terrible mess trying to find all the combinations of sides. I must have been tired and just assumed 6x=180 and 2sinx=1. By that time, I was so mindset that I nearly scolded a person for even saying 90-x. I wonder if this is a case of biased observation that seeks to dis credit me like Jesus of Nazareth since in reality...
View full post »

Similar threads

MHB How do trigonometric functions and their inverses relate to each other?
Replies
16
Views
2K
I Adding trig functions with different amplitudes
Replies
5
Views
2K
B Why do we care about trig identities?
Replies
17
Views
6K
A Trick to Memorizing Trig Special Angle Values Table
Replies
3
Views
1K
MHB Approximating Trig Values using the Unit Circle
Replies
11
Views
3K
A Don't understand this function, s(cosξ + j sinξ) in my textbook
Replies
4
Views
831
B Brushing Up Math Knowledge: Basic Trig Questions
Replies
14
Views
2K
Using Euler's formula to prove trig identities using "sum to product" technique
Replies
4
Views
2K
I Differentiating the Dot Product's Evil Twin
Replies
2
Views
1K
MHB How Can I Evaluate Trig Functions Without a Calculator?
Replies
6
Views
2K

Hot Threads

Recent Insights

Back
Top