Solving Trig Equations with Factoring

Factor the expression sec²x − secx − 2.

• (secx − 2)(secx + 1)

• (secx + 2)(secx - 1)

• (secx - 1)(secx + 2)

• (secx + 1)(secx - 2)

What is the factored form of 2cos²x − 3cosx = 0?

• cosx(2cosx − 3) = 0

• (cosx − 1)(2cosx + 3) = 0

• (2cosx + 3)(cosx − 1) = 0

• cos²x(2 − 3cosx) = 0

Solve the equation 2cos²θ - 1 = 0 for θ in the interval [0, 2π).

• θ = π/4, 3π/4, 5π/4, 7π/4

• θ = π/2, 3π/2, 5π/2, 7π/2

• θ = 0, π, 2π, 3π

• θ = π/6, π/3, 2π/3, 5π/3

How do you convert csc²x to sin²x?

• Use the identity csc²x = 1/sin²x.

• Multiply csc²x by sin²x.

• Add sin²x to csc²x.

• Subtract sin²x from csc²x.

What is the general solution for cosx = a?

• x = ±cos⁻¹(a) + 2kπ, where k is any integer.

• x = ±sin⁻¹(a) + 2kπ, where k is any integer.

• x = ±tan⁻¹(a) + 2kπ, where k is any integer.

• x = a + 2kπ, where k is any integer.

What is the definition of a trigonometric equation?

• An equation that involves trigonometric functions of a variable.

• An equation that only involves linear functions.

• An equation that has no solutions.

• An equation that is always true for any value of the variable.

What is the relationship between the angles in a right triangle and trigonometric functions?

• The ratios of the lengths of the sides of a right triangle define the trigonometric functions.

• The angles in a right triangle are always equal to 90 degrees.

• Trigonometric functions are only applicable to obtuse triangles.

• The angles in a right triangle do not affect the side lengths.

What is the relationship between csc²x and sin²x?

• csc²x = sin²x

• csc²x = 1/sin²x

• csc²x = 2sin²x

• csc²x = sin²x + 1

What is the double angle formula for cosine?

• cos(2x) = cos²x - sin²x

• cos(2x) = 2cos²x - 1

• cos(2x) = 1 - 2sin²x

• cos(2x) = sin²x - cos²x

What is the range of the cosine function?

• [0, 1]

• [-1, 1]

• [-2, 2]

• [1, 2]