Solving "sin 2x = sin 2y" with Double Angle Identity

Click For Summary
SUMMARY

The equation sin 2x = sin 2y can be solved using the double angle identity for sine. The key conclusion from the discussion is that the equality can be expressed as 2x = 2y + nπ, where n is any integer. This relationship allows for the determination of x in terms of y or vice versa, facilitating the solution of the original equation. The double angle identity is essential for transforming the sine function into a linear equation.

PREREQUISITES
  • Understanding of trigonometric identities, specifically the double angle identity for sine.
  • Familiarity with solving equations involving periodic functions.
  • Basic knowledge of integer multiples and their role in trigonometric equations.
  • Ability to manipulate algebraic equations to isolate variables.
NEXT STEPS
  • Study the double angle identities for sine and cosine in detail.
  • Learn how to solve trigonometric equations involving periodic functions.
  • Explore the concept of general solutions for trigonometric equations.
  • Practice problems involving sin and cos identities to reinforce understanding.
USEFUL FOR

Students studying trigonometry, educators teaching trigonometric identities, and anyone looking to enhance their problem-solving skills in mathematics.

Kuma
Messages
129
Reaction score
0

Homework Statement



I'm stuck on a question that results in this equality

sin 2x = sin 2y

how do I solve that for x or y?
the only identity is the double angle one I can use I think but I don't know how that would help.

Homework Equations





The Attempt at a Solution

 
Physics news on Phys.org
Kuma said:

Homework Statement



I'm stuck on a question that results in this equality

sin 2x = sin 2y

how do I solve that for x or y?
the only identity is the double angle one I can use I think but I don't know how that would help.

Homework Equations



The Attempt at a Solution


2x = 2y + n\pi
 

Similar threads

  • · Replies 10 ·
Replies
10
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 26 ·
Replies
26
Views
1K
  • · Replies 10 ·
Replies
10
Views
2K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 18 ·
Replies
18
Views
2K
  • · Replies 6 ·
Replies
6
Views
3K
Replies
5
Views
2K
  • · Replies 11 ·
Replies
11
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K