Moderate -0.3 This is a standard trigonometric equation requiring the compound angle formula for sin(θ-30°), followed by algebraic manipulation and solving a linear trigonometric equation. It's slightly easier than average because it reduces to a straightforward form after expansion, requiring only routine techniques with no geometric insight or complex problem-solving.
Use trig formula and obtain an equation in sinθ and cosθ
M1*
sinθcos30°−cosθsin30°+cosθ=2sinθ
Answer
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Guidance
Obtain an equation in tanθ
M1(dep*)
e.g. tanθ = 1−sin30°
2−cos30°
Can be implied by correct answer following correct expansion.
Otherwise need to see working
( )
Answer
Marks
Guidance
Obtain tanθ=1/ 4− 3 , or equivalent
A1
4+ 3, 0.4409.... (2 s.f or better)
13
Answer
Marks
Guidance
Obtain final answer θ = 23.8° and no others in range
A1
( )
At least 3 sf 23.7939....
ignore extra values outside range
4
Answer
Marks
Guidance
Question
Answer
Marks
Question 2:
2 | Use trig formula and obtain an equation in sinθ and cosθ | M1* | Condone sign error in expansion and/or omission of "+cosθ"
sinθcos30°−cosθsin30°+cosθ=2sinθ
Obtain an equation in tanθ | M1(dep*) | e.g. tanθ = 1−sin30°
2−cos30°
Can be implied by correct answer following correct expansion.
Otherwise need to see working
( )
Obtain tanθ=1/ 4− 3 , or equivalent | A1 | 4+ 3, 0.4409.... (2 s.f or better)
13
Obtain final answer θ = 23.8° and no others in range | A1 | ( )
At least 3 sf 23.7939....
ignore extra values outside range
4
Question | Answer | Marks | Guidance