# Angle sum identities for sine and cosine | Summary and Q&A

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December 28, 2017
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blackpenredpen
Angle sum identities for sine and cosine

## TL;DR

This video demonstrates how to prove the angle sum formula for sine and cosine using a visual representation.

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### Q: How do you define sine and cosine in a right triangle?

In a right triangle, sine is equal to the ratio of the opposite side to the hypotenuse, while cosine is the ratio of the adjacent side to the hypotenuse.

### Q: How can the angle sum formula for sine and cosine be proved?

By constructing a visual representation, the narrator demonstrates that sine alpha plus beta is equal to sine alpha times cosine beta plus cosine alpha times sine beta. Similarly, cosine alpha plus beta is equal to cosine alpha times cosine beta minus sine alpha times sine beta.

### Q: What are the limitations of the angle sum formula for sine and cosine?

The formula only holds true if alpha plus beta is between 0 and 90 degrees. For negative angles or angles greater than 90 degrees, a different approach is required to prove the formula legitimately.

### Q: How can the angle sum formula for sine and cosine be applied in real-world scenarios?

The angle sum formula for sine and cosine is widely used in various fields, such as physics, engineering, and computer graphics, to calculate the effects of combining multiple angles or rotations.

## Summary & Key Takeaways

• The video begins by reviewing the definitions of sine and cosine in a right triangle.

• The narrator constructs a visual representation to prove the angle sum formula for sine and cosine.

• The video explains the steps taken to calculate the values of sine and cosine for angles alpha and beta.

• The narrator concludes by stating the limitations of the formula and acknowledging alternative approaches for negative angles or angles greater than 90 degrees.