Edexcel PMT Mocks — Question 14 8 marks

Exam BoardEdexcel
ModulePMT Mocks (PMT Mocks)
Marks8
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicTrigonometric equations in context
TypeConvert sin/cos ratio to tan
DifficultyStandard +0.3 Part (a) requires applying compound angle formulas and algebraic manipulation to derive a specific tan value, which is standard A-level technique. Part (b) is a straightforward substitution (x=2θ+30°) using the result from (a) to find solutions in a given range. This is a routine multi-step question testing compound angles and equation solving with no novel insight required, making it slightly easier than average.
Spec1.05l Double angle formulae: and compound angle formulae1.05o Trigonometric equations: solve in given intervals

14. Given that $$2 \cos ( x + 60 ) ^ { 0 } = \sin ( x - 30 ) ^ { 0 }$$ a. Show, without using a calculator, that $$\tan x = \frac { \sqrt { 3 } } { 3 }$$ b. Hence solve, for \(0 \leq \theta < 360 ^ { 0 }\) $$2 \cos ( 2 \theta + 90 ) ^ { 0 } = \sin ( 2 \theta ) ^ { 0 }$$

14. Given that

$$2 \cos ( x + 60 ) ^ { 0 } = \sin ( x - 30 ) ^ { 0 }$$

a. Show, without using a calculator, that

$$\tan x = \frac { \sqrt { 3 } } { 3 }$$

b. Hence solve, for $0 \leq \theta < 360 ^ { 0 }$

$$2 \cos ( 2 \theta + 90 ) ^ { 0 } = \sin ( 2 \theta ) ^ { 0 }$$

\hfill \mbox{\textit{Edexcel PMT Mocks  Q14 [8]}}