Why do we add intervals of pi to our solution

The video tutorial explains how to find all solutions for the equation sine of x equals ±1/2. It begins by identifying solutions within the interval [0, 2π] using the unit circle. The tutorial then demonstrates graphing the sine function to visualize these solutions and extends the concept to find all possible solutions by leveraging the periodic nature of the sine function. The instructor highlights the use of adding π to find additional solutions, simplifying the process by avoiding redundancy.

What is the first step in finding all solutions for sine equals plus or minus 1/2?

• Graph the sine function

• Use the unit circle to find solutions between 0 and 2π

• Calculate the derivative of the sine function

• Use a calculator to find approximate solutions

Which angle corresponds to a sine value of plus or minus 1/2 on the unit circle?

• π/2

• π/6

• π/4

• π/3

How many solutions are there for sine equals plus or minus 1/2 between 0 and 2π?

• Five

• Four

• Three

• Two

What is the period of the sine function?

• 4π

• π

• 2π

• 3π

Why is it unnecessary to add 2π to every solution when finding all solutions?

• Because 2π only applies to cosine functions

• Because adding π is sufficient to find all solutions

• Because solutions are only needed in the positive direction

• Because the sine function is not periodic

What happens when you add π to the angle π/6?

• You get a new solution at 7π/6

• You get a new solution at 5π/6

• You get a new solution at 11π/6

• You get a new solution at π/3

How can you represent all solutions for sine equals plus or minus 1/2?

• By adding 2π to each solution

• By adding π to each solution

• By subtracting π from each solution

• By multiplying each solution by 2