Solving for cosine using multiple angles

The video tutorial explains how to solve the equation cosine of 2X equals 1/2. It begins by identifying the angles on the unit circle where cosine equals 1/2, specifically π/3 and 5π/3. The instructor then graphs the cosine function to visualize these solutions and discusses how to find all possible solutions by considering the periodic nature of the cosine function. The tutorial concludes by calculating the distances between solutions and finalizing the solution for X, emphasizing the importance of understanding the unit circle and graphing techniques.

What is the main goal when solving the equation cosine of 2X equals 1/2?

• To determine when cosine equals 0

• To find all possible solutions, not limited to a specific interval

• To find solutions only within the interval of 0 to π

• To solve for sine instead of cosine

Which angles are identified as solutions where cosine equals 1/2?

• π/2 and 3π/2

• π/4 and 3π/4

• π/3 and 5π/3

• π/6 and 5π/6

What is the significance of the initial period of the cosine graph?

• It determines the amplitude of the cosine function

• It helps in identifying the first set of solutions

• It shows the maximum and minimum values of cosine

• It is used to find the sine values

How do you find all solutions for the cosine equation?

• By adding multiples of π to the initial solutions

• By dividing the initial solutions by 2

• By subtracting π from the initial solutions

• By adding multiples of 2π to the initial solutions

What is the distance between each solution in the cosine graph?

• 2π

• π/2

• π

• 3π

What is the final step to find the solutions for X?

• Multiply the solutions by 2

• Add π to the solutions

• Divide the solutions by 2

• Subtract π from the solutions

What are the final solutions for X after dividing by 2?

• π/2 plus 2πN and 3π/2 plus 2πN

• π/4 plus πN and 3π/4 plus πN

• π/3 plus 2πN and 5π/3 plus 2πN

• π/6 plus πN and 5π/6 plus πN