Finding all of the solutions of cosine with a multiple angle

What is the first step in finding all solutions for the equation cosine(X/2) = sqrt(2)/2?

• Find solutions between 0 and π

• Find solutions between 0 and 2π

• Find solutions for all real numbers

• Find solutions between π and 2π

Which angles on the unit circle have a cosine value of sqrt(2)/2?

• π/4 and 7π/4

• π/2 and 3π/2

• π/3 and 5π/3

• π/6 and 11π/6

What does the cosine graph illustrate about the nature of trigonometric solutions?

• They only exist in the positive direction

• They have infinite solutions due to periodicity

• They have a finite number of solutions

• They are limited to one revolution

How do you represent all solutions for the equation cosine(X/2) = sqrt(2)/2?

• By adding 2π to each solution

• By subtracting π from each solution

• By adding π to each solution

• By subtracting 2π from each solution

What is the general form of the solution for X in the equation cosine(X/2) = sqrt(2)/2?

• X = π/4 + 2πN

• X = π/2 + 4πN

• X = π/2 + 2πN

• X = π/4 + 4πN

What is the next step after finding the specific angles π/4 and 7π/4?

• Subtract π to find more solutions

• Add π to find more solutions

• Multiply by 2 to solve for X

• Divide by 2 to solve for X

Why do we add 2πN to the solutions π/4 and 7π/4?

• To limit the solutions to one revolution

• To account for the periodic nature of the cosine function

• To find solutions in the negative direction

• To find solutions only between 0 and 2π