Unlocking Trig Identities: Proving sin(2x + pi/3)

Click For Summary
SUMMARY

The discussion focuses on proving the trigonometric identity sin(2x + π/3) = sin(2x) + sin(2(x + π/3)). Participants emphasize the application of double angle formulas and the sine addition formula. The key step involves recognizing the identity for sin(a) - sin(b) to manipulate the left-hand side effectively. The solution requires careful application of trigonometric identities to arrive at the conclusion.

PREREQUISITES
  • Understanding of trigonometric identities, specifically sine addition formulas.
  • Familiarity with double angle formulas for sine.
  • Knowledge of manipulating algebraic expressions involving trigonometric functions.
  • Basic skills in solving trigonometric equations.
NEXT STEPS
  • Study the sine addition formula in detail, particularly sin(a + b).
  • Review double angle formulas for sine, focusing on sin(2x).
  • Practice problems involving the identity sin(a) - sin(b) to enhance manipulation skills.
  • Explore graphical representations of trigonometric identities for better conceptual understanding.
USEFUL FOR

Students studying trigonometry, mathematics educators, and anyone looking to deepen their understanding of trigonometric identities and their proofs.

iamthegelo
Messages
52
Reaction score
0

Homework Statement



By using trig formulas show that,

sin(2x + pi/3) = sin(2x) + sin(2(x+pi/3))

Homework Equations



Trig Identities

The Attempt at a Solution



I've used double angle formulas, sin(a+b) formulas, I just can't seem to get it.
 
Physics news on Phys.org
It does look like a case for sin(a + b). Can you show us what went wrong when you simply apply the identity for sin(a + b) = sin(a) ... + ... to sin(2x + pi/3) ?
 
write (for the left hand side)
sin(2x + pi/3)=[sin(2x + pi/3)-sin(2x +2pi/3)]+sin(2(x + pi/3))
recall the identity for
sin(a)-sin(b)
 

Similar threads

Replies
21
Views
4K
  • · Replies 10 ·
Replies
10
Views
2K
  • · Replies 4 ·
Replies
4
Views
1K
  • · Replies 6 ·
Replies
6
Views
3K
Replies
4
Views
2K
  • · Replies 1 ·
Replies
1
Views
3K
  • · Replies 7 ·
Replies
7
Views
2K
Replies
5
Views
2K
  • · Replies 10 ·
Replies
10
Views
2K
  • · Replies 3 ·
Replies
3
Views
5K