Activity for cos(a+b) formula

Question 1

Which segment is [math]\cos\alpha[/math]?

Question 2

Which segment is [math]\cos\beta[/math]?

Question 3

Which segment is [math]\sin\alpha[/math]?

Question 04

Which segment is [math]\sin\beta[/math]?

Question 5

Which segment is [math]\cos\left(\alpha+\beta\right)[/math]?

Question 6

Which segment is [math]\sin\left(\alpha+\beta\right)[/math]?

Question 7

What is an expression in terms of [math]\alpha[/math] and [math]\beta[/math] for the length of AB? Hint: Use right triangle ABG.

Question 8

Explain why angle CAD must be congruent to angle GEF?

Question 9

Write an expression in terms of [math]\alpha[/math] and [math]\beta[/math] for the length of FG? Hint: Use right triangle EFG

In question 5, you should have found that segment AI can be calle

Question 10

In question 5, you should have found that segment AI can be called [math]\cos\left(\alpha+\beta\right)[/math] But AI is also the difference of AB-IB=AB-FG. What is another (more complicated) expression for the length of AI?

[math]\cos\alpha\cos\beta-\sin\alpha\sin\beta[/math] [math]\sin\alpha\sin\beta-cos\alpha\cos\beta[/math] [math]\cos\alpha\cos\beta+\sin\alpha\sin\beta[/math]