AP Precalc Review 3.8-3.12

What are the solutions for the equation @@0 = -\text{sqrt}{3}\text{sin}\theta - 2\text{sin}^2\theta@@?

• @@\theta = 0, \text{pi}, \frac{4\text{pi}}{3}, \frac{5\text{pi}}{3}@@

• @@\theta = \frac{\text{pi}}{6}, \frac{5\text{pi}}{6}, \frac{7\text{pi}}{6}, \frac{11\text{pi}}{6}@@

• @@\theta = \frac{\text{pi}}{4}, \frac{3\text{pi}}{4}, \frac{5\text{pi}}{4}, \frac{7\text{pi}}{4}@@

• @@\theta = \frac{\text{pi}}{3}, \frac{2\text{pi}}{3}, \frac{4\text{pi}}{3}, \frac{5\text{pi}}{3}@@

What is the value of 1 - sin²x?

• sin²x

• 1

• cos²x

• tan²x

What is the relationship between sine and cosine in the Pythagorean identity?

• sin²x + cos²x = 1

• sin²x - cos²x = 1

• sin²x + cos²x = 0

• sin²x * cos²x = 1

What is a Pythagorean identity?

• A relation between sine and cosine functions expressed as sin²x + cos²x = 1.

• An equation that defines the relationship between tangent and cotangent functions.

• A formula used to calculate the area of a triangle.

• A theorem that states the sum of the angles in a triangle is 180 degrees.

Which of the following is NOT a Pythagorean identity? sin²x + cos²x = 1, 1 - cos²x = sin²x, 1 - sin²x = cos²x, sin²x - cos²x = -1

• sin²x + cos²x = 1

• 1 - cos²x = sin²x

• 1 - sin²x = cos²x

• sin²x - cos²x = -1

What is the range of values for cosθ when cosθ ≥ -√2/2?

• @@[0, rac{3 ext{pi}}{4}] igcup [rac{5 ext{pi}}{4}, 2 ext{pi})@@

• @@[0, rac{ ext{pi}}{2}] igcup [rac{3 ext{pi}}{2}, 2 ext{pi})@@

• @@[rac{ ext{pi}}{4}, rac{3 ext{pi}}{4}] igcup [rac{5 ext{pi}}{4}, rac{7 ext{pi}}{4}]@@

• @@[0, rac{ ext{pi}}{4}] igcup [rac{3 ext{pi}}{4}, rac{5 ext{pi}}{4}]@@

What is the value of cos²x in terms of sin²x?

• cos²x = 1 - sin²x.

• cos²x = sin²x.

• cos²x = 1 + sin²x.

• cos²x = 2 - sin²x.

What is the value of sin²x in terms of cos²x?

• sin²x = 1 - cos²x.

• sin²x = cos²x.

• sin²x = 2 - cos²x.

• sin²x = 1 + cos²x.

What is the general solution for cosθ = k, where k is a constant?

• θ = ±cos⁻¹(k) + 2nπ, where n is any integer.

• θ = ±sin⁻¹(k) + 2nπ, where n is any integer.

• θ = ±tan⁻¹(k) + 2nπ, where n is any integer.

• θ = k + nπ, where n is any integer.

What is the value of 1 - cos²x?

• sin²x

• cos²x

• 1

• tan²x