SPS SPS SM Pure 2025 February — Question 4 4 marks

Exam BoardSPS
ModuleSPS SM Pure (SPS SM Pure)
Year2025
SessionFebruary
Marks4
TopicQuadratic trigonometric equations
TypeShow then solve: secant/cosecant/cotangent identities
DifficultyStandard +0.3 This is a standard trigonometric equation requiring conversion to a quadratic in sec θ using the identity tan²θ = sec²θ - 1, then solving the resulting quadratic. It's slightly above average difficulty due to the identity manipulation and finding solutions in the full 360° range, but remains a routine textbook exercise with well-established techniques.
Spec1.05h Reciprocal trig functions: sec, cosec, cot definitions and graphs1.05o Trigonometric equations: solve in given intervals

4. In this question you must show all stages of your working. \section*{Solutions relying entirely on calculator technology are not acceptable.} Solve, for \(0 < \theta \leq 360 ^ { \circ }\), the equation $$3 \tan ^ { 2 } \theta + 7 \sec \theta - 3 = 0$$ giving your answers to one decimal place.
(Total for Question 4 is 4 marks)

4. In this question you must show all stages of your working.

\section*{Solutions relying entirely on calculator technology are not acceptable.}
Solve, for $0 < \theta \leq 360 ^ { \circ }$, the equation

$$3 \tan ^ { 2 } \theta + 7 \sec \theta - 3 = 0$$

giving your answers to one decimal place.\\
(Total for Question 4 is 4 marks)\\

\hfill \mbox{\textit{SPS SPS SM Pure 2025 Q4 [4]}}