Determine all of the solutions for a trigonometric equation with cosine and tangent

The video tutorial demonstrates how to solve a trigonometric equation involving cosine and tangent functions. It begins by setting up the problem and moving all variables to one side. The instructor explains the process of factoring and applying the zero product property to separate the equation into solvable parts. The tutorial then covers solving for specific trigonometric functions using the unit circle to find all possible solutions. Finally, it discusses finding general solutions and concludes with a summary of the process.

What is the first step in solving the equation 2 cosine squared of x times tangent of x equals the tangent of x?

• Apply the Pythagorean identities

• Directly solve for x

• Use the quadratic formula

• Get all variables onto the same side

Why can't the terms 2 cosine squared of x times tangent of x and tangent of x be subtracted?

• They are both trigonometric functions

• They are not like terms

• They are equal

• They are already simplified

What property is applied after factoring the equation?

• Pythagorean identity

• Distributive property

• Commutative property

• Zero product property

What are the two cases derived from the zero product property in this problem?

• Tangent of x equals 0 and sine of x equals 1

• Sine of x equals 0 and cosine of x equals 1

• Tangent of x equals 0 and cosine of x equals square root of 2/2

• Tangent of x equals 1 and cosine of x equals 0

How is the tangent of an angle determined using the unit circle?

• By the x-coordinate

• By the y-coordinate

• By the y-coordinate over the x-coordinate

• By the x-coordinate over the y-coordinate

What is the general solution for x when tangent of x equals 0?

• x = πn

• x = π/4 + 2πn

• x = π/2 + 2πn

• x = 2πn

How do you find all solutions for cosine of x equals square root of 2/2?

• By subtracting 2π from each solution

• By adding π to each solution

• By adding 2π to each solution

• By subtracting π from each solution