Finding the exact value for period in radians

In summary, the period of the function f(x) = 6 sin(4x+pi) is 2pi/4, which simplifies to pi/2. This can be found by using the formula Period = 2pi/abs(b) and recognizing that the function can be rewritten as 6 sin(4(x+pi/4)), which has the same period as the original function.
  • #1

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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  • #2
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.
 
  • #3
Thank you
 

1. What is the formula for finding the exact value for period in radians?

The formula for finding the exact value for period in radians is T = 2π/ω, where T represents the period and ω represents the angular frequency.

2. How do you convert a period in seconds to radians?

To convert a period in seconds to radians, you can use the formula T (radians) = 2π/T (seconds). Simply divide 2π by the period in seconds to get the value in radians.

3. Can the value for period in radians be negative?

Yes, the value for period in radians can be negative. This usually occurs when dealing with functions that have a negative angular frequency, resulting in a negative period value.

4. How is the value for period in radians different from the value in degrees?

The value for period in radians is different from the value in degrees because radians are a unit of measurement for angles in the metric system, while degrees are a unit of measurement in the imperial system. Radians are also based on the circumference of a circle, while degrees are based on dividing a circle into 360 equal parts.

5. Why is it important to find the exact value for period in radians?

It is important to find the exact value for period in radians because it allows for more precise calculations and comparisons. Radians are also the preferred unit of measurement in many mathematical and scientific applications, as they are more closely related to the underlying geometry and trigonometry involved.

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