Trigonometric Functions — Class 11 ISC Mathematics revision notes
A 6-page visual revision sheet for Trigonometric Functions, written for Class 11 ISC 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
identities, general solutions and the triangle rules
Angles, and the unit that calculus insists on
- one radian is the angle subtended at the centre by an arc equal in length to the radius, and it is a pure number, not a unit of the same kind as a degree
- π radians = 180 degrees, so multiply by π/180 to go from degrees to radians and by 180/π to come back
- arc length s = r θ and area of a sector = (1/2) r^2 θ, both valid ONLY with θ in radians
- every derivative and every series in later chapters assumes radians, which is why the unit is not a matter of taste
Signs, and the quadrant they live in
- in the first quadrant all six are positive; in the second only sine and cosecant; in the third only tangent and cotangent; in the fourth only cosine and secant
- sin(-θ) = -sin θ and cos(-θ) = cos θ, so sine is odd and cosine even, and tangent is odd
- the allied angle rule: for 90 degrees or 270 degrees the function CHANGES to its co function, and for 180 degrees or 360 degrees it does not; the sign comes from the quadrant the result lands in
- so sin(90 + θ) = cos θ, and cos(180 - θ) = -cos θ, both read off that one rule rather than memorised separately
The identities everything else is built from
- Pythagorean
sin^2 θ + cos^2 θ = 1 - divided by cos^2
1 + tan^2 θ = sec^2 θ - divided by sin^2
1 + cot^2 θ = cosec^2 θ - compound, sine
sin(A ± B) = sin A cos B ± cos A sin B - compound, cosine
cos(A ± B) = cos A cos B ∓ sin A sin B - compound, tangent
tan(A ± B) = (tan A ± tan B) / (1 ∓ tan A tan B)
Page 1 of 6. The full sheet, all 6 pages, opens free in the app.
What this Trigonometric Functions sheet covers
- radian measure
- Angles, and the unit that calculus insists on
- Signs, and the quadrant they live in
- trigonometric functions and identities
- The identities everything else is built from
- Pythagorean
- divided by cos^2
- divided by sin^2
- compound, sine
- compound, cosine
- compound, tangent
- Multiple and half angles
- double, sine
- double, cosine
- double, tangent
- triple
- the t substitution
- half angle from cosine
- Sum to product, and back
- sum of sines
- difference of sines
- sum of cosines
- difference of cosines
- product to sum
- Which way to convert, and when
- The graphs, and what to read from them
- General solutions of trigonometric equations
- sin θ = 0
- cos θ = 0
- tan θ = 0
- sin θ = sin α
- cos θ = cos α
- tan θ = tan α
- Solving without losing roots
- Properties of a triangle
- sine rule
- cosine rule
- projection
- area
- circumradius and inradius
- half angle
- Which triangle rule to reach for
- Standard values, kept straight
- Maximum and minimum without calculus
- 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.