Determining the equation of a trigonometric function

TL;DR

Determine the equation of a trigonometric function from its graph by analyzing the amplitude, period, and whether it is a sine or cosine function.

Transcript

Hello. I'm now going to use the actual Khan Academy website to do some more problems. And this time we're going to go the other way around. We're going to look at the graph of a trigonometric function and we're going to try to figure out the equation. So let's start with the problem we have in front of us. So we have a-- well we don't know if it's ... Read More

Key Insights

• ☺️ The type of function (sine or cosine) can be determined by evaluating the function at x = 0.
• 👈 The amplitude represents the distance between the maximum or minimum points and the x-axis.
• 😥 The period can be calculated by measuring the distance between any two corresponding points on the graph.

Questions & Answers

Q: How can you determine whether a given graph represents a sine or cosine function?

By evaluating the function at x = 0, you can determine which trigonometric function it represents. If f(0) is 0, it is a sine function. If f(0) is 1, it is a cosine function.

Q: What does the amplitude of a trigonometric function represent?

The amplitude represents how much the graph moves above and below the x-axis. It can be found by measuring the distance between the maximum or minimum points and the x-axis.

Q: How can you calculate the period of a trigonometric function from its graph?

The period is the number of radians it takes for the graph to start repeating. It can be found by measuring the distance between any two corresponding points on the graph.

Q: How can the equation of a trigonometric function be determined from its graph?

By examining the amplitude, period, and whether it is a sine or cosine function, the equation can be deduced. The equation will be in the form f(x) = A sin(Bx) or f(x) = A cos(Bx), where A is the amplitude and B is the coefficient of x.

Summary & Key Takeaways

• The type of function (sine or cosine) can be determined by examining the value of the function at x = 0: sine of 0 is 0, while cosine of 0 is 1.

• The amplitude of the function can be found by determining how much it moves above and below the x-axis.

• The period of the graph can be calculated by measuring how many radians it takes for the graph to start repeating.