Trigonometric Functions — Class 11 CBSE Mathematics revision notes
A 3-page visual revision sheet for Trigonometric Functions, written for Class 11 CBSE 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
Trigonometric Functions in one look
the unit circle's ratios, and every identity built from them
Degrees and radians
- one full revolution
360°=2π rad - straight angle
180°=π rad - degrees to radians
θ_rad=θ_deg×π/180
Reciprocal and quotient identities
- reciprocal of sin
cscθ=1/sinθ - reciprocal of cos
secθ=1/cosθ - reciprocal of tan
cotθ=1/tanθ - tan as a quotient
tanθ=sinθ/cosθ
Signs by quadrant: All Sin Tan Cos
- Quadrant I, 0° to 90°: all six ratios positive
- Quadrant II, 90° to 180°: only sin and cosec positive, rest negative
- Quadrant III, 180° to 270°: only tan and cot positive, rest negative
- Quadrant IV, 270° to 360°: only cos and sec positive, rest negative
Domain and range
- sin θ and cos θ: domain is every real θ, range is [-1,1]
- tan θ and sec θ: undefined wherever cos θ=0, that is θ=(2n+1)π/2
- cot θ and cosec θ: undefined wherever sin θ=0, that is θ=nπ
- tan θ and cot θ: range is all of R, with no bound at all
- sec θ and cosec θ: range skips (-1,1) entirely, never a value strictly between -1 and 1
The three Pythagorean identities
- the basic one
sin^2θ+cos^2θ=1 - divide through by cos²θ
1+tan^2θ=sec^2θ - divide through by sin²θ
1+cot^2θ=csc^2θ
Page 1 of 3. The full sheet, all 3 pages, opens free in the app.
What this Trigonometric Functions sheet covers
- Degrees and radians
- one full revolution
- straight angle
- degrees to radians
- Reciprocal and quotient identities
- reciprocal of sin
- reciprocal of cos
- reciprocal of tan
- tan as a quotient
- Signs by quadrant: All Sin Tan Cos
- Quadrant I, 0° to 90°
- Quadrant II, 90° to 180°
- Quadrant III, 180° to 270°
- Quadrant IV, 270° to 360°
- Domain and range
- How sin and cos move
- The three Pythagorean identities
- the basic one
- divide through by cos²θ
- divide through by sin²θ
- Sum and difference formulas
- sine, sum
- sine, difference
- cosine, sum
- cosine, difference
- Tangent, sum and difference
- sum
- difference
- Sum-to-product, one step further
- sine plus sine
- cosine plus cosine
- Where double angle comes from
- Associated angles, read straight off the circle
- Double angle formulas
- sine
- cosine, first form
- cosine, second form
- cosine, third form
- tangent
- Triple angle formulas
- cosine
- Equations
- General solution
- sin θ = sin α
- cos θ = cos α
- tan θ = tan α
- 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 Trigonometric Functions 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.