Unit circle manipulative | Unit circle definition of trig functions | Trigonometry | Khan Academy

TL;DR

Learn how to calculate the sine and cosine of angles using the unit circle definition of trigonometric functions.

Transcript

This here is a screenshot of the Khan Academy unit circle module. And the whole point here is to get you familiar with the unit circle definition of trig functions, which is just an extension of the traditional SOHCAHTOA definition. But the reason why the math world did this is so that we can define the sine and cosines of angles that are 90 degree... Read More

Key Insights

• 👻 The unit circle definition of trigonometric functions allows us to calculate sine and cosine values for angles beyond 90 degrees.
• ❣️ The sine of an angle is the y-coordinate of the corresponding point on the unit circle, while the cosine is the x-coordinate.
• ⭕ Angles measured in radians can also be used with the unit circle, where 2 pi represents a complete revolution around the circle.
• 🫚 The approximate value of square root of 3/2 (0.866) is commonly used in calculations involving the unit circle.

Questions & Answers

Q: What is the purpose of the unit circle definition of trigonometric functions?

The unit circle definition allows us to calculate the sine and cosine of angles beyond 90 degrees or with negative measures, which cannot be done using the traditional definition.

Q: How do you determine the sine of an angle using the unit circle?

To find the sine of an angle, locate the point on the unit circle corresponding to that angle and note its y-coordinate.

Q: How do you calculate the cosine of an angle using the unit circle?

To find the cosine of an angle, locate the point on the unit circle corresponding to that angle and note its x-coordinate.

Q: What is the significance of the approximate value of square root of 3/2 in radians?

The approximate value of square root of 3/2 (0.866) is commonly used for convenience in calculations involving the unit circle, as the exact value is an irrational number.

Summary & Key Takeaways

• The unit circle definition of trigonometric functions extends the traditional SOHCAHTOA definition to include angles beyond 90 degrees and negative angle measures.

• The sine of an angle is the y-coordinate of the point on the unit circle corresponding to that angle.

• The cosine of an angle is the x-coordinate of the point on the unit circle corresponding to that angle.