Knowledge organisers

Trigonometric Functions: CBSE Class 11 Maths knowledge organiser

Everything to know about trigonometric functions on one page: key definitions, the formulas, a worked example, the mistakes to avoid and a checklist of what you should be able to do.

Download the A4 sheet (PDF)

Key definitions

Radian measure: An angle in radians is arc length ÷ radius; π radians = 180°.
Periodic function: A function that repeats: sin x and cos x have period 2π.
Compound angle formula: Expands expressions such as sin(x + y) and cos(x + y).

Key formulas

Radians; arc	\(\pi\text{ rad}=180^\circ;\) \(l=r\theta\)
Pythagorean	\(\sin^2x+\cos^2x=1,\) \(1+\tan^2x=\sec^2x\)
Compound, \(\sin\)	\(\sin(x\pm y)=\sin x\cos y\pm\cos x\sin y\)
Compound, \(\cos\)	\(\cos(x\pm y)=\cos x\cos y\mp\sin x\sin y\)
Compound, \(\tan\)	\(\tan(x\pm y)=\frac{\tan x\pm\tan y}{1\mp\tan x\tan y}\)
Double	\(\sin2x=2\sin x\cos x,\) \(\cos2x=1-2\sin^2x=2\cos^2x-1\)
Double, \(\tan\)	\(\tan2x=\frac{2\tan x}{1-\tan^2x}\)
Triple	\(\sin3x=3\sin x-4\sin^3x,\) \(\cos3x=4\cos^3x-3\cos x\)
\(\sin A+\sin B\)	\(\sin A+\sin B=2\sin\tfrac{A+B}2\cos\tfrac{A-B}2\)
\(\cos A+\cos B\)	\(\cos A+\cos B=2\cos\tfrac{A+B}2\cos\tfrac{A-B}2\)
\(\cos A-\cos B\)	\(\cos A-\cos B=-2\sin\tfrac{A+B}2\sin\tfrac{A-B}2\)
Signs: All, Sin, Tan, Cos in quadrants I to IV; \(\sin,\cos\) period \(2\pi\), \(\tan\) period \(\pi\)

Worked example

Convert \(225^\circ\) to radians.

\(225 \times \dfrac{\pi}{180} = \dfrac{5\pi}{4}\).

Common mistakes

Using degrees in \(l = r\theta\): \(\theta\) must be in radians.
Sign of a ratio in quadrants II to IV taken from the acute-angle value only.
\(\sin(x + y) = \sin x + \sin y\) (false), or \(\cos(x + y)\) with a plus sign between the products.
\(\cos 2x = 2\cos x - 1\): the cosine is squared.

You should be able to…

Convert between degrees and radians, use arc length, and find signs and values of trigonometric functions.
Find all ratios from one, reduce large angles, and use compound-angle and double-angle formulae.
Prove identities with sum-to-product and multiple-angle formulae and answer applied case studies.
Find exact values such as tan(5π/12) and handle chains of identities.

The printable sheet

Trigonometric Functions knowledge organiser for CBSE Class 11 Maths: one A4 page of key definitions, formulas, a worked example and common mistakes — Trigonometric Functions knowledge organiser (CBSE Class 11 Maths), A4. Download the PDF.

Revise it next

Other CBSE Class 11 Maths topics: Sets · Relations and Functions · Complex Numbers and Quadratic Equations · Linear Inequalities · Permutations and Combinations · Binomial Theorem · Sequences and Series · Straight Lines · Conic Sections · Introduction to Three Dimensional Geometry · Limits and Derivatives · Statistics · Probability · All CBSE Class 11 Maths organisers