Trigonometric Functions and Angles

The video tutorial explains how to solve the trigonometric equation 2sin(2x) - √3 = 0 within the interval 0 to 2π radians. It involves recognizing the interval for x, performing a substitution to solve for u, and identifying angles on the unit circle where the sine value is √3/2. The tutorial covers finding angles in the first and second quadrants and converting these solutions back to x. The process includes understanding the unit circle, double angle identities, and solving trigonometric equations.

What is the interval for 2x if x is between 0 and 2π radians?

• 0 to 6π radians

• 0 to 4π radians

• 0 to 2π radians

• 0 to π radians

What substitution is made to simplify the equation 2sin(2x) - √3 = 0?

• u = cos(x)

• u = sin(x)

• u = 2x

• u = x

What is the value of sin(u) when solving the equation 2sin(u) - √3 = 0?

• 0

• 1

• 1/2

• √3/2

Which angle in the first quadrant has a sine value of √3/2?

• π/6 radians

• π/2 radians

• π/3 radians

• π/4 radians

What is the angle in the first quadrant after one full rotation with a sine value of √3/2?

• 5π/3 radians

• 4π/3 radians

• 7π/3 radians

• 2π/3 radians

Which angle in the second quadrant has a sine value of √3/2?

• π/3 radians

• 4π/3 radians

• 3π/3 radians

• 2π/3 radians

What is the angle in the second quadrant after one full rotation with a sine value of √3/2?

• 10π/3 radians

• 8π/3 radians

• 12π/3 radians

• 6π/3 radians

What is the value of x when 2x = π/3 radians?

• π/2 radians

• π/3 radians

• π/6 radians

• π radians

What is the value of x when 2x = 7π/3 radians?

• 7π radians

• 7π/2 radians

• 7π/3 radians

• 7π/6 radians

What is the value of x when 2x = 8π/3 radians?

• 4π/3 radians

• 8π/3 radians

• 2π/3 radians

• π/3 radians