Learn how to find multiple solutions to a trigonometric equation

The video tutorial explains how to solve a trigonometric equation involving cosine squared of 2X. The teacher demonstrates the process of adding and dividing terms to simplify the equation, and then finding solutions for 2X within the range of 0 to 2π. The lesson includes identifying initial solutions and exploring additional solutions by considering the periodic nature of the trigonometric function. The teacher emphasizes understanding the difference between angles and how to find all possible solutions by adding π/4 increments.

What is the first step in solving the equation cosine squared of 2X = 1/2?

• Subtract 1 from both sides

• Multiply both sides by 2

• Add 1 to both sides

• Take the square root of both sides

After simplifying the equation to cosine of 2X = ± sqrt 2 / 2, what is the next step?

• Subtract π from both sides

• Multiply by 2

• Solve for X directly

• Find angles for 2X

What are the initial solutions for X after dividing the angles for 2X by two?

• π/8, 3π/8, 5π/8, 7π/8

• π/4, 3π/4, 5π/4, 7π/4

• π/2, π, 3π/2, 2π

• π/6, π/3, π/2, 2π/3

How do you find additional solutions for X in the range 0 to 2π?

• Multiply each solution by 2

• Subtract π/4 from each solution

• Add π/4 to each solution

• Add π/2 to each solution

What is the maximum value of X for the solutions to remain within 0 to 2π?

• 15π/8

• 11π/8

• 17π/8

• 9π/8