Questions and Answers
What is the formula for sin(α - β)?
What is the formula for cos(2α)?
What is the formula for sin(α + β)?
What is the formula for cos(α - β)?
Signup and view all the answers
What is the formula for sin(2α)?
Signup and view all the answers
What is the formula for cos(α + β)?
Signup and view all the answers
What is the formula for the cosine of a difference?
Signup and view all the answers
Which method is used to derive the formula for $\cos(\alpha + \beta)$?
Signup and view all the answers
What is the formula for the sine of a sum?
Signup and view all the answers
What is the formula for the cosine of a sum?
Signup and view all the answers
What is the purpose of deriving compound angle formulas?
Signup and view all the answers
What is the formula for the sine of a difference?
Signup and view all the answers
Which of the following is not a method used to derive compound angle formulas?
Signup and view all the answers
What is the advantage of using compound angle formulas?
Signup and view all the answers
What is the correct application of the co-function identity in the derivation of the sine of a difference formula?
Signup and view all the answers
Which of the following is a correct application of the compound angle formula for sine?
Signup and view all the answers
What is the result of applying the double angle formula for sine to sin(4α)?
Signup and view all the answers
Which of the following identities is used in the derivation of the cosine of a difference formula?
Signup and view all the answers
What is the difference between the formulas for cos(α - β) and cos(α + β)?
Signup and view all the answers
In deriving the formula for cos(α - β), which of the following is used?
Signup and view all the answers
What is the purpose of using co-functions in the derivation of compound angle formulas?
Signup and view all the answers
Which of the following formulas can be derived using the compound angle formula for cosine?
Signup and view all the answers
What is the purpose of rewriting α + β as α - (-β) in deriving the formula for cos(α + β)?
Signup and view all the answers
Which of the following is a consequence of the even-odd identities?
Signup and view all the answers
What is the relation between the formulas for sin(α - β) and sin(α + β)?
Signup and view all the answers
What is the underlying principle in deriving the formulas for compound angles?
Signup and view all the answers
Why are compound angle formulas useful?
Signup and view all the answers
What is the significance of the method used to derive cos(α + β)?
Signup and view all the answers
If sin(α) = 3/5 and cos(β) = 4/5, what is the value of sin(α - β)?
Signup and view all the answers
If cos(α) = 2/3 and sin(β) = 1/3, what is the value of cos(α + β)?
Signup and view all the answers
If sin(α) = 1/2 and cos(α) = √3/2, what is the value of sin(2α)?
Signup and view all the answers
If cos(α) = 3/5 and sin(α) = 4/5, what is the value of cos(2α)?
Signup and view all the answers
What is the value of sin(α) cos(β) + cos(α) sin(β) in terms of compound angle formulas?
Signup and view all the answers
What is the value of cos(α) cos(β) - sin(α) sin(β) in terms of compound angle formulas?
Signup and view all the answers
What is the key step in deriving the formula for cos(α + β) using the negative angle identity?
Signup and view all the answers
What is the purpose of using the distance formula and cosine rule in deriving the formula for cos(α - β)?
Signup and view all the answers
What is the common feature among the formulas for sin(α - β), sin(α + β), cos(α - β), and cos(α + β)?
Signup and view all the answers
What is the reason for the difference in signs between the formulas for cos(α - β) and cos(α + β)?
Signup and view all the answers
What is the underlying principle behind the derivation of the formulas for compound angles?
Signup and view all the answers
What is the role of the negative angle identity in deriving the formula for cos(α + β)?
Signup and view all the answers
What is the consequence of applying the even-odd identities in the derivation of the formulas for compound angles?
Signup and view all the answers
What is the key idea behind the derivation of the formulas for cos(α - β) and cos(α + β)?
Signup and view all the answers