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12 multiple-choice questions and 25 flashcards on Analytic Trigonometry: Identities and Equations, about 8% of the High School Pre-Calculus bank. Every one carries a written rationale.
Analytic Trigonometry: Identities and Equations is one of 10 chapters in CoStudy's High School Pre-Calculus bank, and it holds 12 of the bank's 150 multiple-choice questions — roughly 8% of the total. That proportion is not arbitrary: chapters follow the certifying body's published exam outline, and the number of questions in each is set by that domain's published weight, so the share of your practice time this chapter takes matches the share of the real exam it accounts for.
Studying by chapter is worth doing once you have a diagnostic score. A single overall percentage tells you whether you are close; it does not tell you which domain is dragging. Working a weak chapter in isolation, and re-testing it in isolation, is the fastest way to move a score that has stalled — and it is why the mock exams in CoStudy report by domain rather than as one number.
3 questions drawn from this chapter, with the full rationale shown — the controlling principle behind the right answer, and why each wrong option tempts and fails.
What is the y-intercept of y = e^x?
Answer: D — 1 (when x=0: e⁰ = 1)
y-intercept: y(0). e⁰ = 1 (any non-zero number to power 0 = 1). All exponential functions y = aˣ (a > 0, a ≠ 1) pass through (0, 1). Pre-Calc exponential properties.
If cos(θ) = 3/5 and θ ∈ Q1, find sin(2θ).
Answer: A — 24/25
A) sin θ = 4/5 (QI, positive). sin(2θ) = 2 sin θ cos θ = 2 · (4/5) · (3/5) = 24/25. B) That is cos(2θ) = 1 − 2sin²θ = 1 − 32/25 = −7/25 absolute value confusion. C) Forgot the factor of 2. D) sin(2θ) cannot exceed 1.
Convert 270° to radians:
Answer: D — 3π/2 (270° · π/180° = 270π/180 = 3π/2)
Conversion: degrees · π/180. 270 · π/180 = 270π/180 = 3π/2. Memorize key conversions: 90°=π/2, 180°=π, 270°=3π/2, 360°=2π. Foundation for trig and calculus.
4 cards from the 25 in this chapter.
State the sum identity for cosine.
cos(α + β) = cos α cos β − sin α sin β.
What is a polar coordinate?
(r, θ) — distance r from origin and angle θ from the positive x-axis.
State the sum identity for sine.
sin(α + β) = sin α cos β + cos α sin β.
When is the Law of Cosines useful?
SAS (two sides + included angle) or SSS (three sides) — when Law of Sines doesn't directly apply.
These are a sample. The full Analytic Trigonometry: Identities and Equations chapter runs 37 items with per-chapter progress tracking, on the web and in the iOS app.
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