Trigonometric Functions and Equations

The video tutorial explains how to solve the trigonometric equation 2 cos x * sin x = sin x within the interval from 0° to 360°, using algebraic techniques. It involves setting the equation to zero, factoring out common terms, and determining angles using the unit circle. The tutorial identifies solutions where sin x equals 0 and cos x equals 1/2, focusing on specific angles in the first and fourth quadrants.

What is the first step in solving the equation 2cos(x)sin(x) = sin(x)?

• Add sin(x) to both sides

• Subtract sin(x) from both sides

• Multiply both sides by 2

• Divide both sides by cos(x)

What common factor can be factored out from the equation 2cos(x)sin(x) - sin(x) = 0?

• 1

• sin(x)

• 2

• cos(x)

When sin(x) is factored out, what is the resulting equation?

• sin(x) * (cos(x) - 2) = 0

• sin(x) * (2cos(x) - 1) = 0

• sin(x) * (cos(x) + 1) = 0

• sin(x) * (2cos(x) + 1) = 0

At which angle does sin(x) equal zero on the unit circle?

• 270°

• 0°

• 180°

• 90°

Which method can be used to find angles where sin(x) = 0?

• Reference triangle method

• Graphical method

• Unit circle method

• Algebraic method

In which quadrants is the cosine function positive?

• First and second

• First and fourth

• Second and third

• Third and fourth

What is the angle in degrees where cos(x) = 1/2 in the first quadrant?

• 90°

• 60°

• 45°

• 30°

What is the angle in degrees where cos(x) = 1/2 in the fourth quadrant?

• 330°

• 300°

• 270°

• 240°

What are the solutions for x in degrees for the equation 2cos(x)sin(x) = sin(x) on the interval [0°, 360°)?

• 0°, 90°, 180°, 270°

• 0°, 60°, 120°, 300°

• 0°, 60°, 180°, 300°

• 0°, 60°, 240°, 300°

Which of the following is not a solution for the equation 2cos(x)sin(x) = sin(x) on the interval [0°, 360°)?

• 0°

• 90°

• 60°

• 180°