MHB Find the sin angle between two 2d vectors

AI Thread Summary
To find the sine angle between two 2D vectors, first calculate cos(theta) using the dot product formula. Once cos(theta) is known, apply the Pythagorean identity sin(theta) = sqrt(1 - cos^2(theta)) to determine sin(theta). This method allows for the calculation of the sine angle without needing direct access to sine values. Understanding this relationship is crucial for solving problems involving angles between vectors. Mastering these concepts will aid in preparing for the math test.
Elissa89
Messages
52
Reaction score
0
Tomorrow is my math test and I'm going over the study guide:

I have vector U=<1, 3> and vector V=<5, 2>

It says let theta be the missing angle between the two vectors. What is the cos(theta) and sin(theta)?

I already know how to find the missing angle for cos(theta) but we never covered how to find the missing angle for sin(theta). It was never in our homework and it's not in my notes but apparently it could be on the test.

So if someone could give me the formula and then show a step by step on how to do this it would be most appreciated.
 
Mathematics news on Phys.org
Once you know \(\cos(\theta)\), then given \(0\le\theta\le\pi\), we may use a Pythagorean identity:

$$\sin(\theta)=\sqrt{1-\cos^2(\theta)}$$
 

Thread 'Non-orthogonal bases'

Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
View full post »

Thread 'Fermat's Last Theorem'

Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
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 »

Similar threads

I Transforming coordinates between Cartesian and spherical
Replies
1
Views
2K
Preservation of the angle between two vectors
Replies
9
Views
2K
MHB Find the angle between 2 vectors w=i+3j, vector v=<5, 2>
Replies
1
Views
2K
B Confusion about the angle between two vectors in a cross product
Replies
7
Views
3K
What is the difference between the two sine rules for resultant vector?
Replies
4
Views
2K
A Finding Minimal Mean Distance Curves on the Unit Sphere
Replies
2
Views
2K
I Geometry and algebraic equations
Replies
4
Views
2K
Torque on a Circular Current Loop under a Misaligned Magnetic Field
Replies
1
Views
981
I Angles between 4-vectors in special relativity?
Replies
5
Views
1K
MHB Use double or half angle formulas
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top