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11 multiple-choice questions and 25 flashcards on Trigonometric Functions, about 7% of the High School Pre-Calculus bank. Every one carries a written rationale.
Trigonometric Functions is one of 10 chapters in CoStudy's High School Pre-Calculus bank, and it holds 11 of the bank's 150 multiple-choice questions — roughly 7% 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.
7 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.
If θ is in Quadrant II and cos(θ) = −3/5, then tan(θ) =
Answer: C — −4/3
C) sin²θ = 1 − 9/25 = 16/25, sin θ = ±4/5. In QII sine is POSITIVE: sin θ = 4/5. tan θ = sin/cos = (4/5)/(−3/5) = −4/3. B) Forgot that tan is negative in QII (only sin is positive there). A) Inverted sin and cos. D) Sign error.
What is the sum of an infinite geometric series with first term 4 and common ratio 1/3?
Answer: B — 6 (S = a/(1-r) = 4/(1-1/3) = 4/(2/3) = 6)
Infinite geometric series converges when |r| < 1. S = a/(1-r) = 4/(1-1/3) = 4/(2/3) = 6. Foundation for Taylor series, calculus.
What is the equation of a circle with center (-2, 3) and radius 5?
Answer: A — (x+2)² + (y-3)² = 25 (center (h,k), radius r: (x-h)² + (y-k)² = r²)
Circle (x-h)² + (y-k)² = r². Center (-2, 3): (x-(-2))² + (y-3)² = (x+2)² + (y-3)². r=5 → r²=25. Sign of h: h=-2 → (x-(-2)) = (x+2).
If sin(θ) = 5/13 and θ is in Quadrant II, then cos(θ) =
Answer: D — −12/13
D) cos²θ = 1 − 25/169 = 144/169 → cos θ = ±12/13. In QII cosine is NEGATIVE, so cos θ = −12/13. A) Forgot the QII sign. B/C) Confused with tan = sin/cos.
Evaluate cos(45) where the argument is in DEGREES.
Answer: A — √2/2 ≈ 0.707
A) cos(45°) = √2/2 ≈ 0.7071. B) Common trap: 45 radians ≈ 2578° (mod 360 ≈ 58°), giving cos ≈ 0.5253 — this is what a calculator in radian mode returns. C) That is cos(90°). D) That is cos(0°).
If the position is x(t) = t² and the position is at t=3, what is x(3)?
Answer: C — 9 (substitute t=3: x(3) = 3² = 9)
Function evaluation: x(3) = 3² = 9. Foundation of parametric thinking. In Pre-Calc and Calc, position functions describe motion. Derivative would give velocity v(t) = 2t.
Convert the polar coordinate (5, π/3) to Cartesian.
Answer: A — (5/2, 5√3/2) (x = r cos θ = 5·(1/2) = 5/2; y = r sin θ = 5·(√3/2) = 5√3/2)
Polar to Cartesian: x = r·cos(θ), y = r·sin(θ). With r=5, θ=π/3: x = 5·cos(π/3) = 5·(1/2) = 5/2; y = 5·sin(π/3) = 5·(√3/2) = 5√3/2. Pre-calc polar coordinates.
4 cards from the 25 in this chapter.
What is sin(45°)?
√2/2.
What is cos(60°)?
1/2.
What are the six trig functions?
sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), cotangent (cot).
What is tan(45°)?
1.
These are a sample. The full Trigonometric Functions chapter runs 36 items with per-chapter progress tracking, on the web and in the iOS app.
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