Trigonometry - 1 — Class 11 Maharashtra HSC Mathematics revision notes
A 4-page visual revision sheet for Trigonometry - 1, 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 - 1 in one look
the unit circle's ratios, extended to any angle at all
Trigonometric Functions and the Unit Circle
- circle radius r, centre at the origin: P(x,y) lies on the terminal ray of angle θ
- cosθ=x/r, sinθ=y/r
- on the unit circle (r=1), P(x,y) is just P(cosθ,sinθ) directly
- ratios are the SAME on the whole terminal ray: independent of r, identical for coterminal angles
Six ratios from x, y, r
- cosine
cosθ=x/r - sine
sinθ=y/r - tangent
tanθ=y/x - cosecant
operatornamecosecθ=r/y - secant
secθ=r/x - cotangent
cotθ=x/y
Where a ratio breaks down
- cosθ=0, i.e. θ=(2n+1)π/2 — tanθ and secθ are undefined there
- sinθ=0, i.e. θ=nπ — cotθ and cosecθ are undefined there
- θ=0 — sinθ=0, cosθ=1, tanθ=0: the base case every identity builds from
- θ=90° — cosθ=0, sinθ=1: tanθ and secθ blow up right here
Page 1 of 4. The full sheet, all 4 pages, opens free in the app.
What this Trigonometry - 1 sheet covers
- Trigonometric Functions and the Unit Circle
- Six ratios from x, y, r
- cosine
- sine
- tangent
- cosecant
- secant
- cotangent
- Where a ratio breaks down
- Signs in Quadrants
- Quadrant I
- Quadrant II
- Quadrant III
- Quadrant IV
- Range of sine and cosine
- Negative Angles
- Negative Angles: even and odd functions
- Ratios from one given value, and a quadrant
- Fundamental Identities
- the basic one
- divide by cos²θ
- divide by sin²θ
- Where the second identity comes from
- Domain and Range
- Periodicity
- Standard Angle Values
- Graphs
- Polar Co-ordinates
- Symbols
- 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 - 1 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.