Trigonometric Functions and Angles

The video tutorial explains how to solve the equation 4 cos(4x) = 2 over a given interval. It uses a substitution method by letting theta = 4x, transforming the equation to 4 cos(theta) = 2. The tutorial then solves for cos(theta) = 1/2 using reference triangles and calculates solutions for x. It highlights the need to find all solutions by considering the periodic nature of the cosine function, resulting in eight solutions. The process is supported by graphical analysis, and the tutorial concludes with a summary of the solution process.

What substitution is used to simplify the equation 4 cos(4x) = 2?

• theta = 2x

• theta = 4x

• theta = x/4

• theta = x/2

What is the cosine value of a 60-degree angle?

• 0

• 1

• sqrt(3)/2

• 1/2

In which quadrants is the cosine function positive?

• Third and Fourth

• First and Second

• First and Fourth

• Second and Third

What is the value of x when theta equals pi/3?

• pi/4

• pi/6

• pi/3

• pi/12

How many complete cycles does the graph of y = cos(4x) have over the interval from 0 to 2pi?

• Four

• Three

• Two

• One

How many solutions are there for the equation cos(4x) = 1/2 over the interval from 0 to 2pi?

• Two

• Four

• Six

• Eight

What is the next coterminal angle to pi/3 when finding additional solutions?

• 5pi/3

• 7pi/3

• 13pi/3

• 11pi/3

What is the value of x when theta equals 5pi/3?

• pi/12

• 5pi/12

• 11pi/12

• 7pi/12

What is the coterminal angle to 11pi/3?

• 23pi/3

• 25pi/3

• 19pi/3

• 17pi/3

How many solutions for x are found in total for the equation 4 cos(4x) = 2?

• Four

• Six

• Ten

• Eight