How to Graph Any Cosine Function | Summary and Q&A

TL;DR

Learn how to graph a cosine function by following a simple step-by-step process using the unit circle.

Key Insights

• 🎮 The video demonstrates a simple and systematic approach to graphing cosine functions.
• 👈 The process involves setting the function between 0 and 2 pi, solving for x, determining the width of sub-intervals, and plotting points.
• 🤩 The unit circle plays a key role in finding cosine values for various angles.
• 📈 Graphing a cosine function does not require shifting, shrinking, or stretching the graph.
• 🤗 The computations involved in graphing can be done by hand, eliminating the need for a calculator.
• 🧡 The range of a cosine function with a coefficient of one-half is from -1/2 to 1/2.
• 👋 Graphing a cosine function follows a repetitive wave pattern.

Transcript

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Questions & Answers

Q: What is the first step in graphing a cosine function?

The first step is to set the function between 0 and 2 pi to determine the interval for graphing.

Q: How do you solve the inequality for x in the given function?

By adding or subtracting the necessary values on both sides of the inequality, you can isolate x and determine the boundaries for graphing.

Q: What is delta x, and how is it calculated?

Delta x represents the width of each sub-interval in the graph. It is calculated by subtracting the lower limit from the upper limit and dividing it by the number of subdivisions (in this case, 4).

Q: Why is the unit circle important in graphing cosine functions?

The unit circle helps determine the x-coordinate values for different angles, which are crucial in calculating the y-values (cosine values) for graph plotting.

Summary & Key Takeaways

• The video provides a step-by-step guide on how to graph a cosine function using the unit circle.

• The first step is to set the function between 0 and 2 pi.

• The video demonstrates how to solve the inequality, find the width of sub-intervals, and plot the points to draw the graph.