Example: Graphing y=3⋅sin(½⋅x)-2 | Trigonometry | Algebra 2 | Khan Academy | Summary and Q&A

TL;DR

This tutorial explains how to graph a sine function with coefficients and shifts by using an interactive widget.

Key Insights

• 🤩 The interactive widget is a helpful tool for graphing functions, allowing users to define key points.
• ☺️ The coefficient on the x term in the sine function affects the growth rate and period of the graph.
• 👨‍💼 Amplitude represents the distance above and below the midline in a sine graph.

Transcript

• [Instructor] So we're asked to graph y is equal to three times sine of 1/2x minus 2 in the interactive widget. And this is the interactive widget that you would find on Khan Academy. And it first bears mentioning how this widget works. So this point right over here, it helps you define the midline, the thing that you could imagine your sine or co... Read More

Questions & Answers

Q: How does the interactive widget help with graphing functions?

The interactive widget helps users define the midline and extreme points used for graphing by allowing them to manipulate these points in the widget.

Q: How does the coefficient affect the graph of sine?

The coefficient on the x term determines the growth rate of the input to sine. In this case, a coefficient of 1/2 reduces the growth rate, doubling the period.

Q: How does the amplitude change in the graph of 3 sine of 1/2x?

The amplitude, which represents the distance above and below the midline, is tripled in the graph of 3 sine of 1/2x compared to the basic sine graph.

Q: What does the minus 2 do in the equation?

The minus 2 in the equation shifts the entire graph downward by two units, meaning that the y-values are all decreased by two.

Summary & Key Takeaways

• The tutorial begins by explaining how the interactive widget works, allowing users to define the midline and extreme points for graphing.

• The basic graph of sine of x is shown, and then the concept of graphing sine of 1/2x is introduced, indicating a slower growth rate and doubled period.

• The amplitude is increased by three in the graph of 3 sine of 1/2x, and then the entire graph is shifted downward by two units.