Understanding Cosine Function Properties

The video tutorial explains how to determine all solutions for the equation cosine of x equals √2/2. It begins with an introduction to the concept of adding 2π to find multiple solutions. The unit circle is used to identify specific angles where cosine equals √2/2, specifically at π/4 and 7π/4. The tutorial then explores the graph of the cosine function, highlighting its periodic nature and how it completes a cycle every 2π. The instructor explains how to find all solutions by considering the periodicity of the cosine function and adding multiples of 2π. The video concludes with a recap of the process and the importance of using 2πn to represent all possible solutions.

Why do we add 2π or n when determining solutions?

• To make the equation more complex

• To account for the periodic nature of trigonometric functions

• To avoid using the unit circle

• To simplify the calculation

What is the cosine of x when x equals π/4?

• √2/2

• 0

• 1

• -1

How does the unit circle help in finding cosine values?

• It simplifies the graph

• It provides a visual representation of angles

• It eliminates the need for calculations

• It only works for sine values

What is the role of the unit circle in trigonometry?

• To provide a geometric representation of angles

• To solve algebraic equations

• To calculate areas

• To measure distances

What is the maximum value of the cosine function?

• -1

• 1

• 0

• √2/2

How many complete cycles does the cosine function have between 0 and 2π?

• Three

• Four

• Two

• One

Why is the graph of cosine considered periodic?

• It is a straight line

• It only has positive values

• It repeats its values at regular intervals

• It has a constant slope

What is the significance of the interval 0 to 2π in trigonometry?

• It is the minimum value

• It represents one complete cycle

• It is the average value

• It is the maximum value

How does the cosine function behave between 0 and 2π?

• It completes one full cycle

• It increases exponentially

• It remains constant

• It decreases linearly

Why is it important to consider the interval beyond 0 to 2π?

• To avoid using the unit circle

• To make the graph more complex

• To find all possible solutions

• To simplify the equation