Trigonometric Equations and Identities

This video tutorial covers solving trigonometric equations using substitution methods, focusing on half-angle and multiple-angle identities. It provides two examples: one involving a cosine equation and another with a sine equation. The tutorial explains how to use trigonometric identities to simplify and solve these equations, and verifies solutions graphically.

What is the primary method used in this lesson to solve trigonometric equations?

• Numerical approximation

• Substitution

• Matrix operations

• Graphical analysis

Which identity is used to substitute for cosine(2x) in the equation cosine(2x) - cosine(x) = 0?

• cosine(2a) = 2cosine^2(a) - 1

• cosine(2a) = 1 - 2sine^2(a)

• cosine(2a) = cosine^2(a) - sine^2(a)

• cosine(2a) = 2sine(a)cosine(a)

In which quadrants is cosine negative?

• Second and third

• Third and fourth

• First and second

• First and fourth

What is the cosine value of a 60-degree angle?

• 1

• 0

• 1/2

• √3/2

What are the solutions for the equation cosine(2x) - cosine(x) = 0 over the interval [0, 2π)?

• π/3, π, 5π/3

• π/6, π/2, 5π/6

• 0, 2π/3, 4π/3

• 0, π/2, π

What is the common factor in the equation sine(x) - sine(2x) = 0?

• tangent(x)

• cosine(x)

• secant(x)

• sine(x)

Which identity is used to substitute for sine(2x) in the equation sine(x) - sine(2x) = 0?

• sine(2a) = 2sine(a)cosine(a)

• sine(2a) = sine^2(a) - cosine^2(a)

• sine(2a) = 1 - 2cosine^2(a)

• sine(2a) = 2cosine(a)sine(a)

What is the sine value at 0 radians on the unit circle?

• 1

• 1/2

• 0

• -1

What are the solutions for the equation sine(x) - sine(2x) = 0 over the interval [0, 2π)?

• 0, π/3, π, 5π/3

• π/4, 3π/4, 5π/4, 7π/4

• π/6, π/2, 5π/6, 3π/2

• 0, π/2, π, 3π/2

Which angle corresponds to 5π/3 radians?

• 60 degrees

• 300 degrees

• 120 degrees

• 240 degrees