Standard +0.3 This is a standard trigonometric equation requiring the identity sin²x = 1 - cos²x to convert to a quadratic in cos x, then solving the quadratic and finding angles in the specified range. It's slightly above average difficulty due to the extended range (360° to 540°) requiring careful consideration of which solutions are valid, but the technique is routine for AS-level students.
Solve, for \(360° \leqslant x < 540°\),
$$12\sin^2 x + 7\cos x - 13 = 0$$
Give your answers to one decimal place.
(Solutions based entirely on graphical or numerical methods are not acceptable.)
[5]
Uses inverse cosine on their values, giving two correct follow
Answer
Marks
Guidance
through values (see note)
M1
1.1b
(cid:159)x(cid:32) 430.5(cid:113), 435.5(cid:113)
A1
1.1b
(5 marks)
Notes:
M1: Uses correct identity
A1: Correct three term quadratic
M1: Solves their three term quadratic to give values for cos x. (The correct answers are
cosx(cid:32) 1 or 1but this is not necessary for this method mark)
3 4
M1: Uses inverse cosine on their values, giving two correct follow through values - may be
outside the given domain
A1: Two correct answers in the given domain
Answer
Marks
Guidance
Question
Scheme
Marks
Question 9:
9 | Uses sin2 x(cid:32)1(cid:16)cos2 x(cid:159) 12(1(cid:16)cos2 x)(cid:14)7cosx(cid:16)13(cid:32)0 | M1 | 3.1a
(cid:159)12cos2 x(cid:16)7cosx(cid:14)1(cid:32)0 | A1 | 1.1b
Uses solution of quadratic to give cos x = | M1 | 1.1b
Uses inverse cosine on their values, giving two correct follow
through values (see note) | M1 | 1.1b
(cid:159)x(cid:32) 430.5(cid:113), 435.5(cid:113) | A1 | 1.1b
(5 marks)
Notes:
M1: Uses correct identity
A1: Correct three term quadratic
M1: Solves their three term quadratic to give values for cos x. (The correct answers are
cosx(cid:32) 1 or 1but this is not necessary for this method mark)
3 4
M1: Uses inverse cosine on their values, giving two correct follow through values - may be
outside the given domain
A1: Two correct answers in the given domain
Question | Scheme | Marks | AOs
Solve, for $360° \leqslant x < 540°$,
$$12\sin^2 x + 7\cos x - 13 = 0$$
Give your answers to one decimal place.
(Solutions based entirely on graphical or numerical methods are not acceptable.)
[5]
\hfill \mbox{\textit{Edexcel AS Paper 1 Q9 [5]}}