Understanding the Solution Set of a Trigonometric Equation

The video tutorial focuses on finding the complete solution set for the equation -6cos(8x) + 4 = 5. It begins by isolating the cosine term and then uses the unit circle and trigonometric identities to expand the solution set. The tutorial explains how to account for all possible solutions by considering the periodic nature of the cosine function. Finally, it demonstrates solving for x and presents the complete solution set, with a promise to evaluate it further in a future video.

What is the first step to isolate the cosine term in the equation?

• Add 4 to both sides

• Subtract 4 from both sides

• Multiply both sides by 6

• Divide both sides by 6

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CCSS.HSF.TF.A.2

What is the value of cosine of an angle in the unit circle?

• The y-coordinate

• The radius

• The x-coordinate

• The angle itself

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CCSS.HSF.TF.C.9

Which identity helps in finding additional solutions for cosine?

• cos(θ) = -cos(θ)

• cos(θ) = tan(θ)

• cos(-θ) = cos(θ)

• cos(θ) = sin(θ)

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CCSS.HSF.TF.A.2

What is the significance of the unit circle in this context?

• It helps in visualizing sine values

• It is used to find all angles with a given cosine

• It is irrelevant to the solution

• It determines the period of the function

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CCSS.HSF.TF.A.4

How does adding 2π to an angle affect its cosine value?

• It negates the cosine value

• It halves the cosine value

• It doubles the cosine value

• It does not change the cosine value

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CCSS.HSF.TF.B.7

What is the general form of the solution for x in terms of inverse cosine?

• x = 8 * cos^(-1)(-1/6) - 2π * n

• x = 1/8 * cos^(-1)(-1/6) - π/4 * n

• x = 8 * cos^(-1)(-1/6) + 2π * n

• x = 1/8 * cos^(-1)(-1/6) + π/4 * n

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CCSS.HSF.TF.B.7

What is the effect of the sign on the 2πn term in the solution?

• It changes the cosine value

• It affects the period of the solution

• It determines the angle's quadrant

• It does not matter as n can be negative

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CCSS.HSF.TF.B.7

In the 'yellow scenario', what is the expression for x?

• x = 1/8 * cos^(-1)(-1/6) + π/4 * n

• x = 1/8 * cos^(-1)(-1/6) - π/4 * n

• x = -1/8 * cos^(-1)(-1/6) + π/4 * n

• x = -1/8 * cos^(-1)(-1/6) - π/4 * n

What is the complete solution set for x?

• Combination of both expressions for x

• Only the first expression for x

• Only the second expression for x

• Neither of the expressions

What will be covered in the future video?

• Graphing the solution set

• Solving a different equation

• Deriving new trigonometric identities

• Evaluating the solution set with a calculator