Playbook
Trigonometry
227 q · 20% HARD · 13 a paper on 2024-2026 papers, up from 8.8. Eight of its ten subtopics are cheap; maximum/minimum (37 q, 35% HARD) and eliminating θ (34 q, 47%) hold 29 of its 46 HARD questions. Bank the eight first, then take the two pools with timed reps.
- Questions in the bank
- 227
- q/paper (21 papers)
- 10.81
- Tagged HARD
- 20%
- Subtopics
- 10
Strand: Cornerstone
When you’ll see it
Ratios of an acute angle, an identity to simplify, or a value given for one expression and asked for another.
How this chapter is tested
The largest chapter in the bank (227 questions) and the one that has grown most: 8.8 questions a paper in 2016-2020, 13.0 on the six 2024-2026 papers. It is Class 10 trigonometry — acute angles, standard values, identities — not the Class 11 general-angle chapter.
Its HARD is pooled. Maximum and minimum values (37 questions, 35% HARD) and eliminating θ (34 questions, 47%) hold 29 of the chapter's 46 HARD questions. The other eight subtopics run between 0% and 18% HARD, so the chapter rewards doing them first.
The sub-skills
The distinct skills inside the chapter, in the order to learn them.
Standard values and ratios
Degree and radian values, and the six ratios read off a right triangle.
Identities
sin²θ + cos²θ = 1 and its two relatives, used to simplify and prove.
The reciprocal pairs
sec θ + tan θ and sec θ − tan θ multiply to 1; the same for cosec θ and cot θ.
Complementary angles
sin(90° − θ) = cos θ and its companions, which collapse long products.
Maximum and minimum
a sin θ + b cos θ lies between −√(a² + b²) and +√(a² + b²); x + 1/x ≥ 2.
Eliminating θ
Given x and y in terms of θ, square and add (or multiply) to remove θ.
Traps to expect
Distractor shapes this chapter reuses. The Traps page covers the ones that cut across chapters.
Impossible values
sin θ = 1.2 or sec θ = 0.5 has no solution; options built on them are distractors.
The reciprocal pair
If sec θ + tan θ = p, then sec θ − tan θ = 1/p, not −p.
Degrees and radians mixed
A radian value placed beside degree options, one of which matches the radian number.
Learn it before you drill it
This chapter has full teaching notes — foundations, worked examples, self-checks and a mastery check for each subtopic. Read the notes once, then drill subtopic by subtopic below.
Trigonometry notesDrill every Trigonometry question
227 questions from the bank, across 10 subtopics.
Drill one subtopic at a time
The 10 subtopics, in teaching order.
- Power Identities and Given SumsDrill Power Identities and Given Sums
- Degree, Radian and Standard ValuesDrill Degree, Radian and Standard Values
- Reciprocal Pairs — sec ± tan and cosec ± cotDrill Reciprocal Pairs — sec ± tan and cosec ± cot
- Complementary and Allied AnglesDrill Complementary and Allied Angles
- Simplifying and Proving IdentitiesDrill Simplifying and Proving Identities
- Compound and Multiple AnglesDrill Compound and Multiple Angles
- Trigonometric EquationsDrill Trigonometric Equations
- Ratios in a Right TriangleDrill Ratios in a Right Triangle
- Maximum, Minimum and Impossible ValuesDrill Maximum, Minimum and Impossible Values
- Eliminating θ and Substitution ChainsDrill Eliminating θ and Substitution Chains
Related playbooks
Often paired with this one — the technique or the trap overlaps. Drill these next.