Knowledge organisers

Introduction to Trigonometry: CBSE Class 10 Maths knowledge organiser

Everything to know about introduction to trigonometry 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

Trigonometric ratio: A ratio of two sides of a right-angled triangle for an acute angle, such as sin A = opposite/hypotenuse.
Trigonometric identity: An equation true for all angles where it is defined, such as sin²A + cos²A = 1.
Complementary angle ratios: sin(90° − A) = cos A and tan(90° − A) = cot A.

Key formulas

Ratios (right \(\triangle\))	\(\sin A=\frac PH,\) \(\cos A=\frac BH,\) \(\tan A=\frac PB=\frac{\sin A}{\cos A}\)
Reciprocals	\(\cosec A=\frac1{\sin A},\) \(\sec A=\frac1{\cos A},\) \(\cot A=\frac1{\tan A}\)
Identities	\(\sin^2A+\cos^2A=1,\) \(1+\tan^2A=\sec^2A,\) \(1+\cot^2A=\cosec^2A\)
\(0^\circ,30^\circ,45^\circ,60^\circ,90^\circ\)	\(\sin:\ 0,\tfrac12,\tfrac1{\sqrt2},\tfrac{\sqrt3}2,1;\) \(\cos:\ 1,\tfrac{\sqrt3}2,\tfrac1{\sqrt2},\tfrac12,0\)
\(\tan\) at the same angles	\(0,\ \tfrac1{\sqrt3},\ 1,\ \sqrt3,\ \text{not defined}\)

Worked example

If \(4\tan\theta=3\), find \(\dfrac{\sin\theta+\cos\theta}{\sin\theta-\cos\theta}\).

\(\tan\theta=\tfrac34\). Take opposite \(=3k\), adjacent \(=4k\), hypotenuse \(=5k\). Then \(\sin\theta=\tfrac35,\ \cos\theta=\tfrac45\), and the expression \(=\dfrac{7/5}{-1/5}=-7\). (Quicker: divide numerator and denominator by \(\cos\theta\) to get \(\dfrac{\tan\theta+1}{\tan\theta-1}=\dfrac{7/4}{-1/4}=-7\).)

Common mistakes

Writing \(\sin A\) as \(\sin\times A\), or \(\sin^2A\) as \(\sin A^2\).
Assuming \(\sin(A+B)=\sin A+\sin B\) — check with \(A=B=30^\circ\): \(\sin 60^\circ\ne 1\).
Mixing up opposite and adjacent sides when the angle is at a different vertex.
Working on both sides of an identity at once as if it were an equation. Start from one side (usually the more complicated one) and reach the other.

You should be able to…

Find all six trigonometric ratios from one given ratio and know the values for 0°, 30°, 45°, 60° and 90°.
Evaluate expressions with standard angles and prove the common identities by working from one side.
Write long answers that combine ratios, standard values and identities, with every substitution shown.
Prove the tougher identities and solve problems where the ratio is given in terms of letters such as a and b.

The printable sheet

Introduction to Trigonometry knowledge organiser for CBSE Class 10 Maths: one A4 page of key definitions, formulas, a worked example and common mistakes — Introduction to Trigonometry knowledge organiser (CBSE Class 10 Maths), A4. Download the PDF.

Revise it next

Other CBSE Class 10 Maths topics: Real Numbers · Polynomials · Pair of Linear Equations in Two Variables · Quadratic Equations · Arithmetic Progressions · Triangles · Coordinate Geometry · Some Applications of Trigonometry · Circles · Areas Related to Circles · Surface Areas and Volumes · Statistics · Probability · All CBSE Class 10 Maths organisers