SPS SPS FM 2022 October — Question 5 7 marks

Exam BoardSPS
ModuleSPS FM (SPS FM)
Year2022
SessionOctober
Marks7
TopicTrigonometric equations in context
TypeSolve shifted trig equation
DifficultyStandard +0.3 Part (a) is a straightforward single-step trig equation requiring inverse cosine and consideration of two solutions in the range. Part (b) requires using the Pythagorean identity to convert to a quadratic in sin(x), then solving - this is a standard A-level technique but involves multiple steps. Both are routine exercises with no novel insight required, making this slightly easier than average.
Spec1.05o Trigonometric equations: solve in given intervals

5. Solve, for \(0 < \theta < 360 ^ { \circ }\),
a) \(5 \cos ( \theta + 30 ) = 3\) b) \(\cos ^ { 2 } ( x ) + 4 \sin ^ { 2 } ( x ) + 4 \sin ( x ) = 0\) Give each non-exact solution to one decimal place.
[0pt]

5. Solve, for $0 < \theta < 360 ^ { \circ }$,\\
a) $5 \cos ( \theta + 30 ) = 3$\\
b) $\cos ^ { 2 } ( x ) + 4 \sin ^ { 2 } ( x ) + 4 \sin ( x ) = 0$

Give each non-exact solution to one decimal place.\\[0pt]
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\hfill \mbox{\textit{SPS SPS FM 2022 Q5 [7]}}