A-LevelMathematicsTrigonometry9709/12 · Oct/Nov 2012 · Q67 Marks
Show that the equation 2 cos x = 3 tan x can be written as a quadratic equation in sin x.
- (i)Show that the equation 2 cos x = 3 tan x can be written as a quadratic equation in sin x.[3]
- (ii)Solve the equation 2 cos 2y = 3 tan 2y, for 0° ≤ y ≤ 180°.[4]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2012). The mark or mark type is shown in brackets.
- [M1] Replaces tan x by sin x / cos x
- [M1] Uses s² + c² = 1. (to convert to sin x only)
- [A1] → 2sin²x + 3sin x - 2 = 0 (AG)
- [M1] Soln of quadratic (for sin 2y)
- [A1] → 2y = 30°
- [DM1] 2y can also be 180 - 30 (or similar for other quadrant)
- [A1] → y = 15° or y = 75°
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