Is sin(nπ) always equal to zero for integer n?

  • Thread starter Thread starter ainster31
  • Start date Start date
  • Tags Tags
    Orthogonal Set
Click For Summary
SUMMARY

The discussion confirms that sin(nπ) is always equal to zero for any integer n. This is established through the fundamental properties of the sine function, specifically its periodic nature and the fact that sine of any integer multiple of π results in zero. The participants emphasize the importance of understanding trigonometric identities to grasp this concept fully.

PREREQUISITES
  • Understanding of trigonometric functions
  • Familiarity with the unit circle
  • Knowledge of periodic functions
  • Basic algebra skills
NEXT STEPS
  • Study the unit circle and its relation to trigonometric functions
  • Learn about the periodic properties of sine and cosine functions
  • Explore trigonometric identities and their proofs
  • Practice solving trigonometric equations involving integer multiples of π
USEFUL FOR

Students studying trigonometry, educators teaching mathematical concepts, and anyone seeking to improve their understanding of trigonometric functions and identities.

ainster31
Messages
158
Reaction score
1

Homework Statement



ZI9L53P.png


Homework Equations


The Attempt at a Solution



zPYzL5K.png


I'm not sure how to prove that it is zero. I don't see what I can do after the second last step.
 
Physics news on Phys.org
What does sin(integer*pi) equal?
 
  • Like
Likes   Reactions: 1 person
arildno said:
What does sin(integer*pi) equal?

It's equal to zero.

Wow. My trigonometry is terrible.
 

Similar threads

Alternative Derivation of sin integral
  • · Replies 3 ·
Replies
3
Views
2K
Fourier sine series integration
  • · Replies 20 ·
Replies
20
Views
3K
Orthogonal trajectories in polar coordinates
  • · Replies 2 ·
Replies
2
Views
3K
Convert the domain of the Tan function to interval notation?
  • · Replies 1 ·
Replies
1
Views
2K
Heat equation problem so confusing
  • · Replies 104 ·
4
Replies
104
Views
8K
Proofs By Induction: Proving P(n) for All n
  • · Replies 3 ·
Replies
3
Views
2K
Fourier Series- half range sine series
  • · Replies 1 ·
Replies
1
Views
2K
Strong Induction: Proving Every Int n>1 is a Product of Primes
  • · Replies 5 ·
Replies
5
Views
2K
PDE: Proving that a set is an orthogonal bases for L2
  • · Replies 13 ·
Replies
13
Views
4K
T/F: Orthogonal matrix has eigenvalues +1, -1
  • · Replies 7 ·
Replies
7
Views
3K