Solving Trigonometric Equations

The video tutorial explains how to solve the equation 2cos(3x) + 1 = 0 over the interval from 0 to 2π radians. It begins by adjusting the interval for 3x, then substitutes u for 3x to simplify the equation. The tutorial identifies solutions on the unit circle where cosine is negative, focusing on the second and third quadrants. Finally, it converts the solutions from u back to x, providing six values of x that satisfy the equation within the given interval.

What is the interval for x in the equation 2cos(3x) + 1 = 0?

• 0 to 2π

• 0 to 4π

• 0 to π

• 0 to 3π

What substitution is made to simplify the equation 2cos(3x) + 1 = 0?

• u = x

• u = 4x

• u = 2x

• u = 3x

In which quadrants is the cosine value negative?

• First and Fourth

• First and Second

• Second and Third

• Third and Fourth

What is the first solution for u in the second quadrant?

• 5π/3

• 4π/3

• 2π/3

• π/3

How many solutions for u are found in the second quadrant within the interval 0 to 6π?

• One

• Two

• Three

• Four

What is the first solution for u in the third quadrant?

• π/3

• 2π/3

• 4π/3

• 5π/3

How many solutions for u are found in the third quadrant within the interval 0 to 6π?

• Two

• Four

• Three

• One

What is the value of x when u = 2π/3?

• 5π/9

• π/9

• 2π/9

• 4π/9

What is the value of x when u = 4π/3?

• 2π/9

• 5π/9

• 4π/9

• π/9

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

• Four

• Eight

• Six

• Two