Is it Correct to Divide Both Angles by 2 in Trigonometry?

  • Thread starter Thread starter Born2Perform
  • Start date Start date
  • Tags Tags
    Trigonometry
AI Thread Summary
Dividing both angles in the trigonometric identity cos(2x) = 2cos^2(x) - 1 is justified through substitution. By letting u = 2x, the identity can be rewritten as cos(u) = 2cos^2(u/2) - 1. This algebraic manipulation allows for the replacement of u with any variable. The underlying principle is based on the properties of cosine and angle manipulation. Thus, the division of angles is mathematically sound in this context.
Born2Perform
Messages
80
Reaction score
0
cos(2x)=2cos^2(x)-1
what algebrical rule guarantees me thet is right to divide both angles for 2:
cos(x)=2cos^2(x/2)-1
 
Mathematics news on Phys.org
Born2Perform said:
what algebrical rule ...

Substitution, nothing more.

cos(2x)=2cos^2(x)-1

Let u=2x, then

cos(u)=2cos^2(u/2)-1

Now you can replace u with whatever pronumeral you desire.
 

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 »
Thread 'Imaginary Pythagorus'

Thread 'Imaginary Pythagorus'

I posted this in the Lame Math thread, but it's got me thinking. Is there any validity to this? Or is it really just a mathematical trick? Naively, I see that i2 + plus 12 does equal zero2. But does this have a meaning? I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero? Ibix offered a rendering of the diagram using what I assume is matrix* notation...
View full post »

Similar threads

B How Do You Derive the Formula for sin(x-y)?
Replies
5
Views
2K
I My attempt to understand horizontal transformations of functions
Replies
6
Views
1K
MHB [ASK]Solution Set of a Trigonometry Inequation
Replies
4
Views
1K
MHB Solving trigonometry equations
Replies
4
Views
2K
I Transforming coordinates between Cartesian and spherical
Replies
1
Views
2K
B To calculate the polar unit vectors using rotated coordinates
Replies
1
Views
2K
MHB Why Does tan(x + pi/2) Equal -cotx in Trigonometry?
Replies
2
Views
2K
I How Can Nested Summation Functions Be Simplified or Reversed?
Replies
6
Views
2K
MHB Proving a trigonometric identity II
Replies
2
Views
2K
MHB Finding the domain of this function.
Replies
5
Views
1K

Hot Threads

Recent Insights

Back
Top