Question 5 - A-Level Maths

Edexcel C2 — Question 5 8 marks

Exam Board	Edexcel
Module	C2 (Core Mathematics 2)
Marks	8
Paper	Download PDF ↗
Mark scheme	Download PDF ↗
Topic	Standard trigonometric equations
Type	Convert to quadratic in sin/cos
Difficulty	Standard +0.3 This is a standard C2 trigonometric equation requiring conversion to a quadratic form using tan x = sin x/cos x, then solving a quadratic equation. The algebraic manipulation is straightforward and the technique is commonly taught. Slightly above average difficulty due to the multi-step nature and need to check which solutions are valid, but still a routine textbook exercise.
Spec	1.02f Solve quadratic equations: including in a function of unknown 1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=1 1.05o Trigonometric equations: solve in given intervals

5. (a) Given that $$8 \tan x - 3 \cos x = 0$$ show that $$3 \sin ^ { 2 } x + 8 \sin x - 3 = 0 .$$ (b) Find, to 2 decimal places, the values of $x$ in the interval $0 \leq x \leq 2 \pi$ such that $$8 \tan x - 3 \cos x = 0 .$$

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(a)

Answer	Marks
$\frac{8\sin x}{\cos x} - 3\cos x = 0$	M1
$8\sin x - 3\cos^2 x = 0$	M1
$8\sin x - 3(1 - \sin^2 x) = 0$
$3\sin^2 x + 8\sin x - 3 = 0$	A1

(b)

Answer	Marks
$(3\sin x - 1)(\sin x + 3) = 0$	M1
$\sin x = -3$ (no solutions) or $\sin x = \frac{1}{3}$	A1
$x = 0.34, \pi - 0.3398$	B1 M1
$x = 0.34, 2.80 \text{ (2dp)}$	A1

**(a)**

$\frac{8\sin x}{\cos x} - 3\cos x = 0$ | M1 |
$8\sin x - 3\cos^2 x = 0$ | M1 |
$8\sin x - 3(1 - \sin^2 x) = 0$ | |
$3\sin^2 x + 8\sin x - 3 = 0$ | A1 |

**(b)**

$(3\sin x - 1)(\sin x + 3) = 0$ | M1 |
$\sin x = -3$ (no solutions) or $\sin x = \frac{1}{3}$ | A1 |
$x = 0.34, \pi - 0.3398$ | B1 M1 |
$x = 0.34, 2.80 \text{ (2dp)}$ | A1 |

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5. (a) Given that

$$8 \tan x - 3 \cos x = 0$$

show that

$$3 \sin ^ { 2 } x + 8 \sin x - 3 = 0 .$$

(b) Find, to 2 decimal places, the values of $x$ in the interval $0 \leq x \leq 2 \pi$ such that

$$8 \tan x - 3 \cos x = 0 .$$

\hfill \mbox{\textit{Edexcel C2  Q5 [8]}}

This paper (9 questions)

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Q1 5 Q2 6 Q3 7 Q4 7 Q5 8 Q6 9 Q7 9 Q8 12 Q9 12

Answer	Marks
\(\frac{8\sin x}{\cos x} - 3\cos x = 0\)	M1
\(8\sin x - 3\cos^2 x = 0\)	M1
\(8\sin x - 3(1 - \sin^2 x) = 0\)
\(3\sin^2 x + 8\sin x - 3 = 0\)	A1

Answer	Marks
\((3\sin x - 1)(\sin x + 3) = 0\)	M1
\(\sin x = -3\) (no solutions) or \(\sin x = \frac{1}{3}\)	A1
\(x = 0.34, \pi - 0.3398\)	B1 M1
\(x = 0.34, 2.80 \text{ (2dp)}\)	A1