Determining the equation of a trig function | Graphs of trig functions | Trigonometry | Khan Academy

TL;DR

The video discusses how to determine the equation of a periodic function based on its midline and amplitude.

Transcript

Write the equation of the function f of x graphed below. And so we have this clearly periodic function. So immediately you might say, well, this is either going to be a sine function or a cosine function. But its midline and its amplitude are not just the plain vanilla sine or cosine function. And we can see that right over here. The midline is hal... Read More

Key Insights

• ❓ The midline of a periodic function is determined by finding the average of the maximum and minimum values.
• ❓ The amplitude measures the distance the function deviates from the midline.
• ☺️ The behavior of the function at x = 0 helps determine whether to use cosine or sine in the equation.
• ☺️ The period of the function is affected by the coefficient in front of x, making it shorter as the coefficient increases.

Questions & Answers

Q: How do you determine the midline of a periodic function?

The midline is the average of the maximum and minimum points of the function.

Q: What is the amplitude of a periodic function?

The amplitude is the distance from the midline to the maximum or minimum point of the function.

Q: How do you decide whether to use cosine or sine in the function equation?

By observing the behavior of the function at x = 0, where cosine(0) = 1 and sine(0) = 0, you can determine which function to use.

Q: How is the period of a function affected by a coefficient in front of x?

The period of the function becomes shorter, taking less time for the argument of the function to reach the same point on the unit circle.

Summary & Key Takeaways

• The function shown in the graph is periodic and can be described using either a cosine or sine function.

• The midline of the function is determined by finding the average of the maximum and minimum points.

• The amplitude of the function is how far it deviates from the midline.

• By considering the behavior of the function at x = 0 and the period of the function, the equation can be determined to be 3 sine(pi/4x - 2).