How to find all the solutions to a trigonometric equation

The video tutorial explains solving a trigonometric equation by applying inverse operations and understanding the unit circle. It covers finding solutions within a specific range and generalizing them to all real solutions using coterminal angles. The importance of considering both positive and negative square roots is emphasized, and the process of rationalizing the denominator is demonstrated.

What is the first step in solving the trigonometric equation discussed in the video?

• Divide both sides by two

• Multiply both sides by two

• Subtract one from both sides

• Add one to both sides

Why is it important to consider both plus and minus when taking the square root in trigonometric equations?

• It simplifies the equation

• It ensures all possible solutions are considered

• It only applies to cosine functions

• It eliminates negative solutions

What is the reference angle for the solutions discussed in the video?

• π/3

• π/2

• π/4

• π/6

How does reflecting a point across the Y-axis affect its coordinates?

• Both coordinates become positive

• Both coordinates become negative

• Only the Y coordinate changes sign

• Only the X coordinate changes sign

What is the significance of the distance between solutions in radians?

• It is always π/3

• It is always π/4

• It is always π/2

• It is always π

How are infinite solutions represented in trigonometric equations?

• By listing all possible angles

• By using a variable to represent coterminal angles

• By using only positive angles

• By using only negative angles

What is the periodic nature of the sine function?

• It repeats every π

• It repeats every 2π

• It repeats every π/2

• It repeats every π/4