- #1
ChickenChakuro
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Homework Statement
What is the period T of [tex]f(t) = cos(3\pi t) + \frac{1}{2}sin(4\pi t)[/tex]
So, I think I have to find the LCD of 3pi and 4pi, which is 12pi. I don't think this is even close to correct though!
I think it is 3. You therefore know that if your cosine portion and your sine portion started off at a certain value each, both will be back at that certain value after t changes by 3.
The period of a function is the length of the interval in which the function repeats itself. In this case, the function f(t) will repeat itself every π seconds. Therefore, the period of this function is π.
The period of a trigonometric function can be calculated by finding the smallest value of t for which the function repeats itself. This can be done by finding the smallest positive value of t for which the cosine or sine function has a value of 1. In this case, the cosine function has a period of 2π and the sine function has a period of π, so the period of the given function is the least common multiple of these two values, which is π.
No, the period of a function cannot be negative. The period of a function is a measurement of time or distance, and these values cannot be negative. However, a function can have a negative period if it is shifted on the x-axis.
The coefficient of the sine or cosine term affects the frequency of the function, which is the number of cycles the function completes in one unit of time. The larger the coefficient, the higher the frequency and the shorter the period will be. In this case, the coefficient of the sine term is 1/2, which means the frequency is half of the cosine term, resulting in a longer period of π.
Yes, the period of a function can change if there is a coefficient or variable that affects the frequency of the function. In this case, if the coefficients of the sine and cosine terms were both changed, the period of the function would also change. Additionally, if the function is shifted on the x-axis, the period will also change.