Trigonometric Functions and Angles

The video tutorial explains how to solve the trigonometric equation 4cos(4x) = 2 over the interval [0, 2π). It begins by expanding the interval for 4x to [0, 8π) and uses substitution to simplify the equation. The tutorial identifies angles with a cosine value of 1/2 using reference triangles and lists all coterminal angles within the interval. It then calculates the solutions for x by multiplying the angles by 1/4. Finally, the solutions are verified graphically by showing intersections of the graphs of y = 4cos(4x) and y = 2.

What is the interval for the angle 4x if x is on the interval from 0 to 2π?

• 0 to 10π

• 0 to 8π

• 0 to 6π

• 0 to 4π

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

• u = 2x

• u = 4x

• u = x/4

• u = x/2

What is the cosine value of the angle in a 30-60-90 triangle?

• 1/2

• √3/2

• 1

• 0

In which quadrants is the cosine value positive?

• Third and fourth

• First and fourth

• Second and third

• First and second

What is the general form for angles u that are coterminal to 1/3π?

• u = 1/3π + πk

• u = 1/3π + 2πk

• u = 1/3π + 3πk

• u = 1/3π + 4πk

What is the next angle after 1/3π + 6π that is greater than 8π?

• 1/3π + 7π

• 1/3π + 8π

• 1/3π + 9π

• 1/3π + 10π

How do you convert the solution from u to x?

• Multiply by 2

• Divide by 2

• Multiply by 1/4

• Divide by 1/4

What is the x value for u = 5/3π?

• 5/10π

• 5/8π

• 5/6π

• 5/12π

How many solutions are there for x in the interval from 0 to 2π?

• 4

• 8

• 6

• 10

What does the graph of y = 4cos(4x) intersect with y = 2?

• 10 points

• 6 points

• 8 points

• 4 points