Finding the exact value for period in radians

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SUMMARY

The exact period of the function f(x) = 6 sin(4x + π) is determined using the formula Period = 2π/|b|, where b is the coefficient of x in the sine function. In this case, b equals 4, leading to a period of 2π/4, which simplifies to π/2. The horizontal translation does not affect the period, confirming that the period remains π/2 regardless of the phase shift introduced by the +π term.

PREREQUISITES
  • Understanding of trigonometric functions and their properties
  • Familiarity with the sine function and its transformations
  • Knowledge of the concept of period in trigonometric functions
  • Basic algebraic skills for simplifying expressions
NEXT STEPS
  • Study the properties of sine functions, focusing on transformations and periodicity
  • Learn about phase shifts in trigonometric functions
  • Explore the derivation and application of the period formula for trigonometric functions
  • Practice problems involving the calculation of periods for various sine and cosine functions
USEFUL FOR

Students studying trigonometry, educators teaching trigonometric functions, and anyone seeking to understand the periodic nature of sine functions and their transformations.

steve snash
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Homework Statement


What is the exact period of the function f(x)= 6 sin (4x+pi)
= a sin (b)

Homework Equations


Period= 2pi/(abs b)


The Attempt at a Solution


I found the period as 2pi/(4+pi), this is said to be no the correct answer, how do you simplify this down so it is the exact value?
 
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steve snash said:

Homework Statement


What is the exact period of the function f(x)= 6 sin (4x+pi)
= a sin (b)

Homework Equations


Period= 2pi/(abs b)


The Attempt at a Solution


I found the period as 2pi/(4+pi), this is said to be no the correct answer, how do you simplify this down so it is the exact value?
6 sin(4x + pi) = 6 sin(4 (x +pi/4))

What's the period of y = 6 sin(4x)? It's the same as your function. The difference between this function and yours is that one is a horizontal translation of the other.
 
Thank you
 

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