Reduce the trigonometry before solving
Expressions involving \(\sin x+\cos x\) or \(\sin^2x\) often become a one-variable algebra problem after a standard identity. Range questions are then handled by restricting that variable to \([-1,1]\).
For equations on a stated interval, solve the algebraic condition first and count angles second. This prevents missing branches or double-counting endpoints.
Triangle logic matters
The sine rule can produce an ambiguous case, so data do not always determine one triangle. The cosine rule, triangle inequality and inverse/converse Pythagoras are useful for deciding whether a triangle is possible, unique, acute, right or obtuse.
Keep angles in radians when the problem is expressed that way, and do not switch modes mentally during a multi-stage question.
FREE PRACTICE
Try these TMUA-style questions
These questions now draw from the current reviewed CF Maths banks, including image and diagram items where appropriate. Open the solution only after you have committed to a route.
QUESTION 1 · Trigonometric equations & root countingShow answer & route
Answer: B
Correct answer: \(B\). This item is marked from the validated final 200-question answer key. Revision method: Trigonometric equations & root counting. Rework the displayed question carefully and compare your algebra with the keyed option.
Show answer & route
Answer: B
Correct answer: \(B\). This item is marked from the validated final 200-question answer key. Revision method: Trigonometric geometry. Rework the displayed question carefully and compare your algebra with the keyed option.
Show answer & route
Answer: B
Correct answer: \(B\). This item is marked from the validated final 200-question answer key. Revision method: Identities & exact trigonometric values. Rework the displayed question carefully and compare your algebra with the keyed option.
Show answer & route
Answer: C
Correct answer: \(C\). This item is marked from the validated final 200-question answer key. Revision method: Trigonometric geometry. Rework the displayed question carefully and compare your algebra with the keyed option.
Show answer & route
Answer: C
Correct answer: \(C\). This item is marked from the validated final 200-question answer key. Revision method: Trigonometric geometry. Rework the displayed question carefully and compare your algebra with the keyed option.
Show answer & route
Answer: C
Correct answer: \(C\). This item is marked from the validated final 200-question answer key. Revision method: Trigonometric geometry. Rework the displayed question carefully and compare your algebra with the keyed option.
Show answer & route
Answer: B
Correct answer: \(B\). This item is marked from the validated final 200-question answer key. Revision method: Trigonometric geometry. Rework the displayed question carefully and compare your algebra with the keyed option.
Show answer & route
Answer: B
Correct answer: \(B\). This item is marked from the validated final 200-question answer key. Revision method: Trigonometric geometry. Rework the displayed question carefully and compare your algebra with the keyed option.
