Edexcel C2 — Question 7 10 marks

Exam BoardEdexcel
ModuleC2 (Core Mathematics 2)
Marks10
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicTrigonometric equations in context
TypeSolve shifted trig equation
DifficultyStandard +0.3 Part (a) is a straightforward shifted tan equation requiring calculator use and understanding of periodicity. Part (b) requires algebraic manipulation (dividing by cos y, considering cos y = 0 separately) and recognizing standard angle values, making it slightly above average but still a standard C2 exercise with clear techniques.
Spec1.05o Trigonometric equations: solve in given intervals
7. (a) Find, to 2 decimal places, the values of \(x\) in the interval \(0 \leq x < 2 \pi\) for which $$\tan \left( x + \frac { \pi } { 4 } \right) = 3 .$$ (b) Find, in terms of \(\pi\), the values of \(y\) in the interval \(0 \leq y < 2 \pi\) for which $$2 \sin y = \tan y .$$
AnswerMarks Guidance
(a) \(x + \frac{4}{x} = 1.2490, r + 1.2490 = 1.2490, 4.3906\)B1 M1
\(x = 0.46, 3.61\) (2dp)M1 A1
(b) \(2\sin y \cos y = \sin y\)M1
\(\sin y(2\cos y - 1) = 0\)M1
\(\sin y = 0\) or \(\cos y = \frac{1}{2}\)A1
\(y = 0, \pi\) or \(\frac{\pi}{3}, 2\pi - \frac{\pi}{3}\)B1 M1
\(y = 0, \frac{\pi}{3}, \pi, \frac{5\pi}{3}\)A1 (10) 
**(a)** $x + \frac{4}{x} = 1.2490, r + 1.2490 = 1.2490, 4.3906$ | B1 M1 |

$x = 0.46, 3.61$ (2dp) | M1 A1 |

**(b)** $2\sin y \cos y = \sin y$ | M1 |

$\sin y(2\cos y - 1) = 0$ | M1 |

$\sin y = 0$ or $\cos y = \frac{1}{2}$ | A1 |

$y = 0, \pi$ or $\frac{\pi}{3}, 2\pi - \frac{\pi}{3}$ | B1 M1 |

$y = 0, \frac{\pi}{3}, \pi, \frac{5\pi}{3}$ | A1 | **(10)**
7. (a) Find, to 2 decimal places, the values of $x$ in the interval $0 \leq x < 2 \pi$ for which

$$\tan \left( x + \frac { \pi } { 4 } \right) = 3 .$$

(b) Find, in terms of $\pi$, the values of $y$ in the interval $0 \leq y < 2 \pi$ for which

$$2 \sin y = \tan y .$$

\hfill \mbox{\textit{Edexcel C2  Q7 [10]}}
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