Section 9.5: Solving Trigonometric Equations

What is the period of the sine and cosine functions?

• π

• 4π

• 2π

• π/2

Which function has a period of π?

• Sine

• Cosine

• Tangent

• Cosecant

What is the solution for cosθ = -1/2 in the interval [0, 2π)?

• θ = π/3, 5π/3

• θ = π/4, 3π/4

• θ = 2π/3, 4π/3

• θ = π/6, 5π/6

How do you express all possible solutions for a trigonometric function where the period is 2π?

• sinθ = sin(θ ± 2kπ)

• cosθ = cos(θ ± kπ)

• tanθ = tan(θ ± πk)

• cscθ = csc(θ ± 2kπ)

What is the general solution for the equation sinθ = 1/2?

• θ = π/2 ± 2πk, 3π/2 ± 2πk

• θ = π/4 ± 2πk, 3π/4 ± 2πk

• θ = π/3 ± 2πk, 2π/3 ± 2πk

• θ = π/6 ± 2πk, 5π/6 ± 2πk

Which identity is used to solve the equation cos(x - 2x) = 3/2?

• Difference Formula for Cosine

• Double Angle Identity

• Pythagorean Identity

• Sum-to-Product

What is the correct expression for solving quadratic trigonometric equations?

• All of the above

• Set each factor equal to zero

• Use the quadratic formula

• Substitute trigonometric expressions with variables

Which function's inverse will return an angle only in quadrants I or II?

• Cosecant

• Sine

• Cosine

• Tangent

What is the domain of the tangent function?

• All real numbers

• All real numbers except integer multiples of π

• All real numbers except odd integer multiples of π/2

• All real numbers except even integer multiples of π

Which formula would you use to solve the equation 2cos²θ + 3cosθ - 1 = 0?

• Sum-to-Product formulas

• Power-reducing formulas

• Half-angle formulas

• Quadratic formula