O-LevelAdditional MathematicsTrigonometry4037/22 · May/June 2025 · Q910 Marks
Solve the equation 3 sec 3x = √3 cosec 3x for -120° ≤ x ≤ 120°.
- (a)Solve the equation 3 sec 3x = √3 cosec 3x for -120° ≤ x ≤ 120°.[5]
- (b)Solve the equation 2 cos(y+π/3)sin(y+π/3) = sin(y+π/3) for 0 ≤ y < 2π.[5]
Mark scheme
Marking points from the official mark scheme (May/June 2025). The mark or mark type is shown in brackets.
- [B2] tan 3x = √3/3 or 1/√3 or 0.57735... (B1 for 3/cos3x = √3/sin3x oe)
- [M1] Finds one correct and valid triple angle (May be in radians for this mark, implied by one correct value of x)
- [A2] x: 10, 70, -50, -110 and no extras in range (A1 for any two correct angles ignoring extras)
- [B1] sin(y+π/3)=0
- [B1] cos(y+π/3)=1/2
- [M1] Finds one correct and valid compound angle (May be in degrees for this mark)
- [A2] y: 0, 2π/3, 4π/3, 5π/3 oe, nfww (A1 for any two correct angles ignoring extras)
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