Why ratios work
Size does not matter
Two right triangles with the same acute angle are similar, so their side ratios are identical.
↳ That is why the ratios are worth naming.
📚 Chapter Learning Kit
Introduction to Trigonometry · Class 10 Mathematics
English 3 topics 173 leveled MCQs 60 flashcards 3 games Free
Shared by a Veda teacher · Generated with Veda AI · Sep 2026
⚡ Veda Bites
💡 Key Idea
⚙️ Process
➗ Formula
➗ Formula
🧠 Memory Trick
💡 Key Idea
The whole idea, one bite at a time
Veda Bites are swipeable micro-lessons — each one teaches exactly one idea. Here's a taste from this kit; the app has the full deck.
Naming from the angle
Which side is which
↳ Opposite and adjacent SWAP if you switch angles.
The three main ratios
SOH-CAH-TOA
↳ Three letters, three ratios.
Five angles, three rows
The whole table
↳ Learn this and most of the chapter follows.
Remembering the sine row
One list, not three
Write $\sqrt{\frac04}, \sqrt{\frac14}, \sqrt{\frac24}, \sqrt{\frac34}, \sqrt{\frac44}$.
↳ Cosine is the same list reversed.
Why you learn only one row
Cosine is sine backwards
Reading the sine row right to left gives the cosine row.
↳ And tan = sin ÷ cos, so that row is free.
📖 Smart notes
What you'll study, topic by topic
1
The Six Trigonometric Ratios
In a right triangle, each pair of sides forms a ratio, and each ratio depends only on the acute angle — not on how big the triangle is. Three of those ratios are named sine, cosine and tangent; the other three are simply…
- In a right triangle, $\sin A = \frac{\text{opposite}}{\text{hypotenuse}}$, $\cos A = \frac{\text{adjacent}}{\text{hypotenuse}}$,…
- The HYPOTENUSE is always the side facing the right angle, whichever acute angle you are working with.
- 'Opposite' and 'adjacent' are named RELATIVE TO THE ANGLE, and they swap when you switch angles.
~45 min · full explanation, examples & memory tricks in the app
2
Ratios of 0°, 30°, 45°, 60° and 90°
Five angles turn up so often that their ratios are worth knowing by heart. They are not arbitrary: 45° comes from a square cut in half, 30° and 60° from an equilateral triangle cut in half, and 0° and 90° from letting a…
- $\sin$ runs $0,\ \frac12,\ \frac{1}{\sqrt2},\ \frac{\sqrt3}{2},\ 1$ for $0°, 30°, 45°, 60°, 90°$.
- $\cos$ runs the SAME list BACKWARDS: $1,\ \frac{\sqrt3}{2},\ \frac{1}{\sqrt2},\ \frac12,\ 0$.
- $\tan$ runs $0,\ \frac{1}{\sqrt3},\ 1,\ \sqrt3,\ \text{undefined}$.
~45 min · full explanation, examples & memory tricks in the app
3
The Three Trigonometric Identities
One identity, $\sin^2\theta + \cos^2\theta = 1$, follows straight from Pythagoras. Dividing it through by $\cos^2\theta$ and then by $\sin^2\theta$ produces the other two. Together they turn almost any trigonometric expr…
- IDENTITY 1: $\sin^2\theta + \cos^2\theta = 1$, true for every angle.
- IDENTITY 2: $\sec^2\theta - \tan^2\theta = 1$, valid for $0° \le \theta < 90°$.
- IDENTITY 3: $\operatorname{cosec}^2\theta - \cot^2\theta = 1$, valid for $0° < \theta \le 90°$.
~50 min · full explanation, examples & memory tricks in the app
❓ Leveled MCQ practice
Try the smart MCQs from this kit
173 questions laddered from warm-up to topper-level, each with an explanation. A taste:
In a right triangle, the hypotenuse is the side
Beginner
A facing the chosen acute angle
B touching the chosen angle
C facing the right angle
D that is shortest
Show answer & explanation
facing the right angle
It is always the longest side, and it never changes with the angle.
$\sin A$ is defined as
Beginner
A $\frac{\text{adjacent}}{\text{hypotenuse}}$
B $\frac{\text{opposite}}{\text{hypotenuse}}$
C $\frac{\text{opposite}}{\text{adjacent}}$
D $\frac{\text{hypotenuse}}{\text{opposite}}$
Show answer & explanation
$\frac{\text{opposite}}{\text{hypotenuse}}$
SOH — Sine, Opposite, Hypotenuse.
$\cos A$ is defined as
Beginner
A $\frac{\text{opposite}}{\text{hypotenuse}}$
B $\frac{\text{adjacent}}{\text{hypotenuse}}$
C $\frac{\text{adjacent}}{\text{opposite}}$
D $\frac{\text{hypotenuse}}{\text{adjacent}}$
Show answer & explanation
$\frac{\text{adjacent}}{\text{hypotenuse}}$
CAH — Cosine, Adjacent, Hypotenuse.
$\tan A$ is defined as
Beginner
A $\frac{\text{opposite}}{\text{hypotenuse}}$
B $\frac{\text{adjacent}}{\text{opposite}}$
C $\frac{\text{opposite}}{\text{adjacent}}$
D $\frac{\text{adjacent}}{\text{hypotenuse}}$
Show answer & explanation
$\frac{\text{opposite}}{\text{adjacent}}$
TOA — Tangent, Opposite, Adjacent.
🃏 Flashcards
Tap a card to flip it
60 flashcards in this kit — the app reviews them with spaced repetition so the right card returns on the right day.
🎮 Learning games
Play your way through this kit
Every game is built from this kit's own content — scores feed your mastery, so playing counts as studying.
Word Match
True False
Fill Blank
Playable in the app
Study it properly — free, in the app
The full Veda Bites deck, complete notes, spaced-repetition flashcards, leveled MCQs, tests and games for this kit — plus Daily Facts and the Arena, every day.