AP Precalc AB Sem2 Exam: Quiz 4

Complete the sentence. Let x be any real number.

1 + ___ = csc²x

• sec²x

• cot²x

• sin²x

• cos²x

Complete the sentence so the result is an identity. Let x be any real number:

cos x = (cot x)(___)

• sec x

• tan x

• sin x

• csc x

Write the expression in terms of sine and cosine, and simplify so that no quotients appear in the final expression:

tan x (cot x - cos x)

• -sec² x

• 0

• 1 - sin x

• 1

• sec x

• -sec x

• csc x

• 1

Find the exact value of the real number y.

y = arctan (1)

• 2π/3

• π/3

• π/4

• 3π/4

Find the exact value of the real number y.

y = arcsec (-1)

• 2π

• π

• π/2

• 0

• {0, π, π/3, 5π/3}

• {0, π, π/3, 2π/3}

• {0, π, 4π/3, 5π/3}

• {0, π, 3π/2}

Determine the solution set of each equation in radians (for x) or degrees (for θ) to the nearest tenth as appropriate:

4 sin² x - 1 = 0

• {π/3 + nπ, 5π/3 + nπ}

• {π/3 + nπ, 5π/6 + nπ}

• {π/6 + nπ, 5π/6 + nπ}

• {π/6 + nπ, π/2 + 2nπ}