Trigonometry — Class 9 Maharashtra SSC Mathematics revision notes
A 3-page visual revision sheet for Trigonometry, written for Class 9 Maharashtra SSC 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 in one look
the first meeting with the ratios: naming the sides, the standard angles, and one identity
Naming the three sides
- the ratios are defined only in a right angled triangle, and only for one of its two acute angles
- the hypotenuse is the side opposite the right angle. It is the longest side and never changes, whichever acute angle is chosen
- the opposite side is the one facing the chosen angle, not touching it at all
- the adjacent side is the one touching the chosen angle that is not the hypotenuse
- switch to the other acute angle and opposite and adjacent trade places, while the hypotenuse stays put
- so the very first step in any question is to mark the angle you are working with
The six ratios
- sine
sinθ = opp/hyp - cosine
cosθ = adj/hyp - tangent
tanθ = opp/adj - cosecant, reciprocal of sine
cscθ = hyp/opp - secant, reciprocal of cosine
secθ = hyp/adj - cotangent, reciprocal of tangent
cotθ = adj/opp
Why the ratios depend only on the angle
- take two right triangles with the same acute angle but different sizes
- they have two equal angles apiece, the right angle and that acute angle, so they are similar
- in similar triangles corresponding sides are in the same ratio
- so the ratio of opposite to hypotenuse is identical in both, however large or small each triangle is
- that is why sin 30° has one fixed value rather than depending on which triangle it is measured in
- it also means the ratios have no units, being lengths divided by lengths
Page 1 of 3. The full sheet, all 3 pages, opens free in the app.
What this Trigonometry sheet covers
- Trigonometric ratios
- Opposite and adjacent side
- Hypotenuse
- Naming the three sides
- The six ratios
- sine
- cosine
- tangent
- cosecant, reciprocal of sine
- secant, reciprocal of cosine
- cotangent, reciprocal of tangent
- Why the ratios depend only on the angle
- The standard angles
- Where those values come from
- Finding every ratio from one
- Fundamental identity
- The identity, and how it is used
- Complementary angles
- Symbols in this chapter
- 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 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.