Solving Trigonometric Equations

The video tutorial explains how to solve a trigonometric equation by factoring and using the unit circle. It covers setting the equation to zero, factoring, solving for sine and cosine, and verifying solutions graphically. The tutorial also discusses expressing all solutions, including coterminal angles.

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

• Divide both sides by sin(x)

• Multiply both sides by cos(x)

Why should we not divide both sides of the equation by sin(x)?

• It would change the interval of the solution

• It would introduce extraneous solutions

• It would eliminate some solutions

• It would make the equation more complex

After factoring the equation, what are the two conditions we need to solve?

• cos(x) = 1 and sin(x) = 0

• cos(x) = 0 and sin(x) = 1

• sin(x) = 0 and 2cos(x) - 1 = 0

• 2sin(x) = 1 and cos(x) = 0

What is the value of cos(x) when solving 2cos(x) - 1 = 0?

• 1/2

• -1/2

• 1

• 0

Which angles on the unit circle have a sine value of 0?

• 0° and 180°

• 180° and 360°

• 90° and 270°

• 0° and 90°

At which angles does cos(x) equal 1/2 on the unit circle?

• 30° and 330°

• 60° and 300°

• 90° and 270°

• 45° and 315°

How can the solutions be verified graphically?

• By plotting y = 2sin(x) and y = cos(x)

• By plotting y = 2cos(x)sin(x) and y = sin(x)

• By plotting y = cos(x) and y = sin(x)

• By plotting y = tan(x) and y = sin(x)

What do the points of intersection on the graph represent?

• The maximum values of the functions

• The solutions to the equation

• The minimum values of the functions

• The asymptotes of the functions

What is the general form for angles coterminal to 60°?

• x = 60 + 180n

• x = 60 + 360n

• x = 60 + 90n

• x = 60 + 270n

How can all solutions to the equation be expressed?

• Using only the angles 90° and 270°

• Using coterminal angles with multiples of 180° and 360°

• Using only the angles 0°, 60°, 180°, and 300°

• Using coterminal angles with multiples of 90°