Activity for sin(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 GB? Hint: Use right triangle ABG.

Question 8

If angle CAD is [math]\alpha[/math] degrees what can you say about the measure of angle FEG?

Question 9

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

Question 10

In question 6, you should have found that segment EI can be called [math]\sin\left(\alpha+\beta\right)[/math]. But EI is also the sum of EF+FI=EF+GB. What is another (more complicated) expression for the length of EI?

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