Trigonometric Equations and Angles

This video tutorial covers solving trigonometric equations by factoring, focusing on finding solutions within the interval 0 to 2π. It begins with an introduction to the problem, followed by the application of trigonometric identities to simplify the equation. The tutorial then demonstrates the factoring process, setting each factor to zero, and solving for the variable. Finally, it identifies the solutions within the specified interval, providing a comprehensive understanding of the process.

What is the interval within which we are finding solutions for the trigonometric equations?

• 0 to π

• π to 2π

• 0 to 2π

• 0 to 4π

Which trigonometric identity is used to solve the equation 2sin^2 = 1 + cosX?

• sin^2 + cos^2 = 1

• 1 + cot^2 = csc^2

• tan^2 + 1 = sec^2

• sin^2 - cos^2 = 1

What is the first step in transforming the equation 2sin^2 = 1 + cosX?

• Subtract cosX from both sides

• Use the identity sin^2 = 1 - cos^2

• Multiply both sides by 2

• Add 1 to both sides

After transforming the equation, what is the next step?

• Divide by 2

• Add cosX to both sides

• Factor the equation

• Subtract 1 from both sides

What are the factors of the equation after transformation?

• (cosX + 1)(2cosX - 1)

• (2cosX + 1)(cosX - 1)

• (cosX - 1)(2cosX + 1)

• (2cosX - 1)(cosX + 1)

What is the solution for the factor 2cosX - 1 = 0?

• cosX = 1/2

• cosX = -1/2

• cosX = 1

• cosX = -1

At which angle does cosX equal 1/2 in the interval 0 to 2π?

• π/3

• π/2

• π

• 2π/3

In which quadrant is the angle 5π/3 located?

• Quadrant II

• Quadrant I

• Quadrant III

• Quadrant IV

What is the solution for the factor cosX + 1 = 0?

• cosX = 1

• cosX = 0

• cosX = -1

• cosX = 1/2

At which angle does cosX equal -1 in the interval 0 to 2π?

• π

• π/2

• 3π/2

• 2π