9709 · 3.3
Trigonometry flashcards
Revision flashcards for Cambridge 9709 Trigonometry (syllabus 3.3). Flip, recall, then mark a real past-paper question.
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What is the definition of sec(x)?
sec(x) is the secant of x, defined as 1/cos(x). It is undefined when cos(x) = 0.
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What is the definition of csc(x) (or cosec(x))?
csc(x) is the cosecant of x, defined as 1/sin(x). It is undefined when sin(x) = 0.
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What is the definition of cot(x)?
cot(x) is the cotangent of x, defined as 1/tan(x), which is equivalent to cos(x)/sin(x). It is undefined when sin(x) = 0.
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State the Pythagorean identity involving sec(x).
1 + tan²(x) ≡ sec²(x). This is derived by dividing sin²(x) + cos²(x) ≡ 1 by cos²(x).
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State the Pythagorean identity involving cot(x).
1 + cot²(x) ≡ csc²(x). This is derived by dividing sin²(x) + cos²(x) ≡ 1 by sin²(x).
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What are the three forms of the double angle formula for cos(2A)?
1. cos²(A) - sin²(A)\n2. 2cos²(A) - 1\n3. 1 - 2sin²(A)
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When expressing a sin(θ) + b cos(θ) as R sin(θ + α), what are the formulae for R and α?
R = √(a² + b²)\ntan(α) = b/a
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What is the principal value range for y = arcsin(x)?
-π/2 ≤ y ≤ π/2 (or -90° ≤ y ≤ 90°). The output is in quadrants 1 and 4.
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What is the principal value range for y = arccos(x)?
0 ≤ y ≤ π (or 0° ≤ y ≤ 180°). The output is in quadrants 1 and 2.
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What is the principal value range for y = arctan(x)?
-π/2 < y < π/2 (or -90° < y < 90°). The output is in quadrants 1 and 4.
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Common mistake: When solving tan²(x) = 3, what is a frequently missed step?
Forgetting the ± sign when taking the square root. tan(x) = ±√3, leading to solutions in all four quadrants.