Video: Math 168 Precalculus II (Trigonometry) Quiz 2 — Vocabulary Flashcards

Vocabulary flashcards covering inverse trig values, sine subtraction, a trigonometric identity, and solving a double-angle equation based on the lecture notes.

Arcsec (inverse secant) and principal value

Arcsec is the inverse of the secant function. For |x| ≥ 1, sec^-1(x) yields an angle in the interval [0, π] with θ ≠ π/2. Example: sec^-1(2) = 60° (π/3).

Arcsin of sine and principal value

sin^-1(sin x) returns the angle y in [−π/2, π/2] whose sine matches sin x. It maps x to its principal value. Example: sin^-1(sin(7π/5)) = −2π/5.

Sine difference identity

sin(A − B) = sin A cos B − cos A sin B. This is used to simplify expressions like sin(275°)cos(50°) − cos(275°)sin(50°).

Evaluation via sine difference

sin(275°)cos(50°) − cos(275°)sin(50°) = sin(275° − 50°) = sin(225°) = −√2/2.

Cotangent and cosecant product identity

cot θ = cos θ / sin θ and csc θ = 1 / sin θ, so 1 + cot θ csc θ = csc θ (sin θ + cos θ). This follows from distributing csc θ: csc θ sin θ + csc θ cos θ = 1 + cot θ csc θ.

Solutions to cos(2θ) = √3/2 on [0, 2π)

Since 2θ = ±π/6 + 2kπ, the solutions in 0 ≤ θ < 2π are θ = π/12, 11π/12, 13π/12, and 23π/12.