Trigonometry — Class 10 Maharashtra SSC Mathematics revision notes
A 4-page visual revision sheet for Trigonometry, written for Class 10 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
ratios of the sides of a right triangle, the identities they satisfy, and heights measured without climbing
The six ratios, defined from one angle
- fix an acute angle θ in a right angled triangle. The side opposite θ, the side adjacent to it and the hypotenuse are then all decided
- the hypotenuse is always the side opposite the right angle and never changes whichever acute angle is chosen
- the adjacent side is the one touching θ that is not the hypotenuse
- these are ratios of lengths, so they have no units and depend only on the angle, not on the size of the triangle
- that independence is exactly why similar triangles all give the same value for a given angle
The definitions and their reciprocals
- sine, opposite over hypotenuse
sinθ = opp/hyp - cosine, adjacent over hypotenuse
cosθ = adj/hyp - tangent, opposite over adjacent
tanθ = opp/adj - cosecant, the reciprocal of sine
cscθ = 1/sinθ - secant, the reciprocal of cosine
secθ = 1/cosθ - cotangent, the reciprocal of tangent
cotθ = 1/tanθ = cosθ/sinθ
The standard angles, which must be known cold
| θ | sin θ | cos θ | tan θ |
|---|---|---|---|
| 0° | 0 | 1 | 0 |
| 30° | 1/2 | √3/2 | 1/√3 |
| 45° | 1/√2 | 1/√2 | 1 |
| 60° | √3/2 | 1/2 | √3 |
| 90° | 1 | 0 | not defined |
Page 1 of 4. The full sheet, all 4 pages, opens free in the app.
What this Trigonometry sheet covers
- Trigonometric ratios
- Sine cosine tangent
- The six ratios, defined from one angle
- The definitions and their reciprocals
- sine, opposite over hypotenuse
- cosine, adjacent over hypotenuse
- tangent, opposite over adjacent
- cosecant, the reciprocal of sine
- secant, the reciprocal of cosine
- cotangent, the reciprocal of tangent
- The standard angles, which must be known cold
- Trigonometric identities
- Fundamental identity
- Where the three identities come from
- The identities in the forms actually used
- the fundamental identity
- rearranged, which is how it usually appears
- the secant identity
- the cosecant identity
- complementary angles, sine becomes cosine
- and tangent becomes cotangent
- Proving an identity
- How to attack an identity you have not seen
- Angle of elevation
- Angle of depression
- Heights and distances
- A height from one angle
- 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.