Convert polar coordinates to rectangular coordinates | Summary and Q&A

TL;DR

Learn how to convert polar coordinates to rectangular coordinates using the formulas x = r * cos(theta) and y = r * sin(theta).

Key Insights

• 🐻‍❄️ Polar coordinates are represented as (r, theta), where r is the distance from the origin and theta is the angle.
• ❣️ The formulas x = r * cos(theta) and y = r * sin(theta) are used to convert polar coordinates to rectangular coordinates.
• ❣️ The x-coordinate represents the horizontal distance from the origin, while the y-coordinate represents the vertical distance.
• 👨‍💼 Converting polar coordinates to rectangular coordinates involves using trigonometric functions cosine and sine.
• ❣️ Negative values for r indicate a direction opposite to the positive x-axis or positive y-axis.
• 👻 The conversion from polar to rectangular coordinates allows for a more precise location description.
• 🐻‍❄️ There is only one rectangular coordinate representation for a given polar coordinate.

Transcript

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Questions & Answers

Q: How are polar coordinates represented?

Polar coordinates are represented as (r, theta), where r is the distance from the origin and theta is the angle.

Q: What formulas are used to convert polar coordinates to rectangular coordinates?

The formulas used are x = r * cos(theta) and y = r * sin(theta).

Q: How does the x-coordinate represent the horizontal distance?

The x-coordinate represents the horizontal distance from the origin.

Q: What does the y-coordinate represent in rectangular coordinates?

The y-coordinate represents the vertical distance from the origin.

Summary & Key Takeaways

• Polar coordinates are represented as (r, theta), where r is the distance from the origin and theta is the angle.

• To convert polar coordinates to rectangular coordinates, use the formulas x = r * cos(theta) and y = r * sin(theta).

• The x-coordinate represents the horizontal distance and the y-coordinate represents the vertical distance.