billy1024 said:
The period of a trigonometric function is the length of one complete cycle of the function. It is the distance along the x-axis where the function repeats itself. For example, the period of the sine function is 2π, which means it repeats every 2π units along the x-axis.
To find the period of a trigonometric function, you can use the formula 2π/b, where b is the coefficient of the variable in the function. For example, in the function f(x) = 3sin(2x), the coefficient of x is 2, so the period would be 2π/2 = π.
No, the period of a trigonometric function cannot be negative. The period is a measure of the distance along the x-axis, so it must be a positive value. If the coefficient of the variable is negative, the period can be expressed as a negative value, but it is equivalent to the positive value in terms of the function's behavior.
No, not all trigonometric functions have the same period. The period of a function depends on the coefficient of the variable and can vary between different trigonometric functions. For example, the period of the cosine function is 2π, while the period of the tangent function is π.
The frequency of a trigonometric function is the number of cycles it completes in one unit of time. The period and frequency are inversely related, meaning that as the period increases, the frequency decreases. This can be seen in the formula for frequency, where frequency = 1/period.