If k = 2π/45, what is the period?
in general, the period of sin(kx) is 2π/k
so, if k = 2π/45, then the period is
(2π)/(2π/45) = 45
If you are talking about something like sin (2 pi t/45)
a period is from sin (0) to sin (2 pi)
[ also like from pi to 3 pi but keep it simple]
in other words once around the circle
so from (2 pi t/45) = 0 to (2 pi t/45) = 2 pi
or
from t = 0 to t = 45
which is 45 seconds or centuries or whatever.
Ah, math! The period, my dear friend, is like a pesky fly that just won't go away. In this case, with k = 2π/45, it represents a small angle. So small, it's almost as if it's trying to escape its responsibilities as a full-fledged period!
But fear not! The period is actually the length of time it takes for a function to complete one full cycle. In this case, since k is a small angle, the period is quite large, but it's still there. It's just stretching its lazy limbs, enjoying some extra time off.
So, my dear inquirer, the period with k = 2π/45 is simply an elongated affair. But rest assured, it's still there, haunting math problems just like that pesky fly I mentioned earlier.
To find the period of a function with a given value of 'k', you need to use the formula:
Period (T) = 2π / |k|
In this case, k = 2π/45, so the period is:
T = 2π / |2π/45|
To simplify, we can rewrite the absolute value as a positive value, so:
T = 2π / (2π/45)
Now, to divide by a fraction, we can multiply by its reciprocal, so:
T = 2π * (45/2π)
The 2π in the numerator and denominator cancel each other out, leaving:
T = 45
Therefore, the period of the function when k = 2π/45 is 45.
To find the period, we need to use the formula T = 2π/|k|, where k is the coefficient of the angle in a trigonometric function.
In this case, k = 2π/45. To find the period, we need to take the absolute value of k, so |k| = |2π/45| = 2π/45.
Now, we can plug this value into the period formula: T = 2π/|k| = 2π/(2π/45) = 45.
Therefore, the period of the function is 45.