A-LevelMathematicsTrigonometry9709/12 · Feb/Mar 2019 · Q78 Marks
Solve the equation 3 sin²2θ + 8 cos 2θ = 0 for 0° ≤ θ ≤ 180°.
- (a)Solve the equation 3 sin²2θ + 8 cos 2θ = 0 for 0° ≤ θ ≤ 180°.[5]
- (b)The diagram shows part of the graph of y = a + tan bx, where x is measured in radians and a and b are constants. The curve intersects the x-axis at (−π/6, 0) and the y-axis at (0, √3). Find the values of a and b. [Figure X.X][3]
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Mark scheme
Marking points from the official mark scheme (Feb/Mar 2019). The mark or mark type is shown in brackets.
- [M1] 3(1-cos²2θ) + 8 cos 2θ = 0 → 3cos²2θ-8cos 2θ-3 (= 0)
- [A1] cos 2θ = -1/3 soi
- [A1] 2θ = 109.(47)° or 250.(53)°
- [A1A1ft] θ = 54.7° or 125.3°
- [B1] √3 = a + tan0 → a = √3
- [M1] 0 = tan(−bπ / 6) + √3 taken as far as tan⁻¹, angle units consistent
- [A1] b=2
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