Trigonometry - 2 — Class 11 Maharashtra HSC Mathematics revision notes
A 5-page visual revision sheet for Trigonometry - 2, written for Class 11 Maharashtra HSC Mathematics. Formulas, diagrams and the traps that cost marks, laid out to be read the night before rather than the term before. Free, and it opens inside CapCompass.
Page 1 as PDF
Trigonometry - 2 in one look
sums, differences, doubles and triples of angles, folded back into single ratios
Compound Angles
- a compound angle: A+B or A-B, treated as a single angle
- cos(A-B)=cos Acos B+sin Asin B
- cos(A+B)=cos Acos B-sin Asin B
- get cos(A+B) from cos(A-B) by putting -B in place of B, since cos(-B)=cosB and sin(-B)=-sinB
Where cos(A-B) comes from
- on the unit circle put P at angle A and Q at angle B: P(cos A,sin A), Q(cos B,sin B)
- squared chord length by the distance formula: [d(PQ)]^2=2-2(cos Acos B+sin Asin B)
- now measure the SAME chord after turning the axis so OQ becomes the new x-axis: the angle between the rays is A-B, so P becomes (cos(A-B),sin(A-B)) and Q becomes (1,0)
- that gives the same chord as [d(PQ)]^2=2-2cos(A-B)
- **a chord's length does not depend on where the axes point**, so the two expressions are equal: cos(A-B)=cos Acos B+sin Asin B
Sum and Difference Formulae
- sine
sin(A+B)=sin Acos B+cos Asin B - sine
sin(A-B)=sin Acos B-cos Asin B - tangent
tan(A+B)=tan A+tan B/1-tan Atan B - tangent
tan(A-B)=tan A-tan B/1+tan Atan B - cotangent
cot(A+B)=cot Acot B-1/cot B+cot A - cotangent
cot(A-B)=cot Acot B+1/cot B-cot A
Page 1 of 5. The full sheet, all 5 pages, opens free in the app.
What this Trigonometry - 2 sheet covers
- Compound Angles
- Where cos(A-B) comes from
- Sum and Difference Formulae
- sine
- tangent
- cotangent
- Getting cos15° from a compound angle
- Values at 15° and 75°
- sin15°, cos15°
- tan15°
- sin75°, cos75°
- tan75°
- Allied Angles
- Allied Angle Results
- The odd-even rule for allied angles
- Multiple Angles
- Double Angle Formulae
- cosine
- cos2θ: pick the form that matches what's given
- Double Angle continued: the half-angle substitution
- Factorisation: two directions of the same four identities
- sum/difference → product
- product → sum/difference
- Angles of a Triangle
- Symbols
- Triple Angle Formulae
- sin 2 theta and cos 2 theta from one given ratio
- Traps that cost marks
- Tricks that save time
How CapCompass uses this sheet
These notes are not a standalone PDF. CapCompass plans Mathematics chapter by chapter against your real exam dates and free hours, and when the plan reaches Trigonometry - 2 the sheet opens inside the study block itself — at the page covering the sub-topic that block is on, with the timer still running. Revision arrives at the moment the plan says revise, instead of having to be gone looking for.