Trigonometric Functions and Equations

The video tutorial explains how to solve a trigonometric equation over the interval from 0 to 2 pi. It begins with a substitution using trigonometric identities to simplify the equation. The process involves isolating sin^2 x and solving for sin x by taking the square root. The tutorial then demonstrates finding angles where the sine function values are either positive or negative, using a calculator for decimal approximations. The video concludes with identifying four solutions within the specified interval.

What is the interval over which the given trigonometric equation is solved?

• 0 to 4π

• π to 2π

• 0 to 2π

• 0 to π

Which identity is chosen for substitution in the equation?

• cosine 2θ = 2sin²θ - 1

• cosine 2θ = 1 - 2sin²θ

• cosine 2θ = cos²θ - sin²θ

• cosine 2θ = 2cos²θ - 1

After substitution, what is the next step in simplifying the equation?

• Multiply both sides by 2

• Add constants to both sides

• Clear the parentheses

• Divide both sides by 2

What is the value of sin²x after isolating it in the equation?

• 1/6

• 1/3

• 1/2

• 1/4

What is the reference angle used for finding solutions when sinx is negative?

• 0.425 radians

• 0.5 radians

• 0.3 radians

• 0.6 radians

In which quadrants is the sine function negative?

• First and Second

• Second and Third

• Third and Fourth

• First and Fourth

What is the approximate value of the angle in the third quadrant where sinx is negative?

• 2.7211 radians

• 3.5621 radians

• 5.8627 radians

• 4.7124 radians

What is the reference angle used for finding solutions when sinx is positive?

• 0.3 radians

• 0.425 radians

• 0.5 radians

• 0.6 radians

In which quadrants is the sine function positive?

• First and Second

• Second and Third

• Third and Fourth

• First and Fourth

How many solutions are found for the equation over the given interval?

• Five

• Four

• Three

• Two