Trigonometric Function Expansion Techniques

The video tutorial covers sine and cosine expansions, focusing on selecting the appropriate expansion based on the signs and order of functions. It provides examples to illustrate these concepts and discusses reordering functions and using auxiliary angle forms. The tutorial emphasizes the importance of choosing the right expansion to simplify calculations and avoid unnecessary complexity.

What is the primary reason for choosing a specific sine or cosine expansion?

• To match the coefficients exactly

• To avoid using trigonometric identities

• To simplify the expression

• To fit the structure of the given problem

Why might it be unwise to choose an expansion with a minus sign?

• It complicates the calculation

• It requires additional steps to simplify

• It results in larger angles

• All of the above

What is a common feature of trigonometric functions that often appear in expansions?

• They never include negative signs

• They are always positive

• They frequently include square roots

• They always have integer coefficients

What happens to angles when you choose an expansion with a double negative?

• They disappear

• They become larger

• They remain unchanged

• They become smaller

What is the benefit of using smaller angles in trigonometric expansions?

• They are more accurate

• They are easier to work with

• They simplify the expression

• They reduce calculation time

When given an expression with sine first and a minus sign, which expansion should you consider?

• An expansion with cosine first and a minus sign

• An expansion with sine first and a plus sign

• An expansion with sine first and a minus sign

• An expansion with cosine first

Which function should you use if cosine is the first function in the expression?

• An expansion with a minus sign

• An expansion with cosine first

• An expansion with a plus sign

• An expansion with sine first

What should you consider first when choosing an expansion for a trigonometric expression?

• The presence of square roots

• The coefficients of sine and cosine

• The function that appears first

• The overall length of the expression

How can you rewrite an expression to use a different auxiliary angle form?

• By using a different trigonometric identity

• By reordering the terms

• By swapping sine and cosine

• By changing the coefficients

What should you do if you notice a cosine at the front of an expression?

• Use a sine expansion

• Ignore the cosine

• Use a cosine expansion

• Reorder the expression