Trigonometric Functions and Their Properties

In this AP daily practice session, teachers Becky Barnes and J Sadiki introduce Unit 3, focusing on trigonometry and polar functions. They discuss periodic functions, sinusoidal functions, and transformations, providing real-world examples. The session includes example problems involving sinusoidal function modeling and a clock face. A review of trigonometric functions, including tangent and reciprocal functions, is also provided. The session concludes with an invitation to future sessions.

Who are the teachers presenting this session?

• Michael Green and Sarah White

• Alice Johnson and Bob Brown

• John Doe and Jane Smith

• Becky Barnes and J Sadiki

What is the main focus of Unit 3?

• Trigonometry and Polar Functions

• Algebra and Geometry

• Probability and Combinatorics

• Calculus and Statistics

Which of the following is an example of periodic behavior?

• A constant speed

• A school year calendar

• A car accelerating

• A linear function

What is a key characteristic of sinusoidal functions?

• They are linear

• They have a repeating pattern

• They are always increasing

• They have no maximum or minimum

What does the 'a' value represent in sinusoidal transformations?

• Horizontal shift

• Vertical dilation

• Frequency

• Phase shift

In the example problem, what is the period length found?

• 15

• 6

• 9

• 12

What is the relationship between tangent and sine/cosine?

• Tangent is the product of sine and cosine

• Tangent is cosine divided by sine

• Tangent is the sum of sine and cosine

• Tangent is sine divided by cosine

Where do vertical asymptotes occur for the function h(θ) = tan(3θ) + 1?

• At θ = π/3 + πk

• At θ = π/6 + π/3k

• At θ = π/4 + π/2k

• At θ = π/2 + πk