How to find the period of an equation?

Understand the Problem

The question is asking how to determine the period of a mathematical equation, likely involving trigonometric functions such as sine or cosine, which have repeating intervals.

Answer

The period is given by $ \frac{2\pi}{|k|} $ where $k$ is the coefficient of $x$.

Steps to Solve

Identify the Function Begin by identifying the trigonometric function involved in the equation. Common functions are $y = \sin(kx)$ or $y = \cos(kx)$, where $k$ is a constant.
Determine the Value of k The period of a sine or cosine function is modified by the coefficient $k$. The standard period of $y = \sin(x)$ or $y = \cos(x)$ is $2\pi$. To find the new period, you need to determine the value of $k$ from the equation.
Calculate the New Period To find the period of the function, use the formula for the period, which is given by:

$$ \text{Period} = \frac{2\pi}{|k|} $$

Substituting the value of $k$ from step 2 will yield the period of the function.

Evaluate the Result After performing the necessary calculations, review your result to ensure it's accurate. The period indicates how far along the x-axis you have to go for the function to repeat itself.

The period of $y = \sin(kx)$ or $y = \cos(kx)$ is given by

$$ \text{Period} = \frac{2\pi}{|k|} $$

where $k$ is the coefficient of the variable $x$ in the function.

More Information

The concept of the period in trigonometric functions is crucial in various fields, such as physics, engineering, and signal processing. Understanding periods helps in modeling periodic phenomena like sound waves and alternating currents.

Tips

Misidentifying k: Sometimes, students misinterpret the equation and do not correctly identify the coefficient $k$. Always double-check the form of the function.
Forgetting absolute value: Not taking the absolute value of $k$ can lead to incorrect results, especially if $k$ is negative.

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