Trigonometric Functions and Equations

The video tutorial explains how to solve the equation 4cos(4x) = 2 over a given interval. It discusses why using a double angle identity is not ideal and instead suggests letting theta equal 4x. The tutorial then solves for theta using a 30-60-90 triangle to find where cosine equals 1/2. It identifies the relevant angles in radians and converts these solutions back to x, resulting in x = π/12 and x = 5π/12.

What is the initial equation that needs to be solved?

• 4 * sin(4x) = 2

• 4 * sec(4x) = 2

• 4 * cos(4x) = 2

• 4 * tan(4x) = 2

Why is using a double angle identity not recommended in this problem?

• It is not applicable to cosine functions.

• It requires additional variables.

• It makes the equation more complex.

• It only works for sine functions.

What substitution is made to simplify the equation?

• theta = 4x

• theta = 3x

• theta = 2x

• theta = 5x

What is the cosine value that needs to be found for theta?

• 1

• 1/2

• 1/3

• 1/4

Which triangle is used to determine the cosine value?

• 45-45-90 triangle

• Isosceles triangle

• Equilateral triangle

• 30-60-90 triangle

In which quadrants is the cosine function positive?

• First and second

• Third and fourth

• First and fourth

• Second and third

What is the reference angle in radians for 60 degrees?

• pi/4

• pi/3

• pi/6

• pi/2

What is the value of theta in the fourth quadrant?

• 3pi/3

• 4pi/3

• 5pi/3

• 2pi/3

What is the final solution for x when theta equals pi/3?

• x = pi/4

• x = pi/3

• x = pi/12

• x = pi/6

What is the final solution for x when theta equals 5pi/3?

• x = 5pi/6

• x = 5pi/4

• x = 5pi/12

• x = 5pi/3