Class 10 • Maths • Chapter 8
INTRODUCTION TO TRIGONOMETRY
True & False Quiz
Opposite. Adjacent. Hypotenuse.
✓True
✗False
25
Questions
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Ch.8
Chapter
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X
Class
Why True & False for INTRODUCTION TO TRIGONOMETRY?
How this format sharpens your conceptual clarity
🔵 Trigonometry is the bridge between angles and lengths — used in navigation, architecture, and physics worldwide.
✅ T/F tests standard angle values (0°, 30°, 45°, 60°, 90°), reciprocal ratios, and the fundamental identity.
🎯 tan 90° is UNDEFINED (not zero or infinity in the standard sense) — a repeated T/F trap in CBSE.
📋
Read each statement carefully. Click True or False — instant feedback with explanation appears. Submit anytime; unattempted questions are marked Skipped.
Q 1
In a right triangle, if an acute angle is \(\theta\), then \(\sin \theta = \dfrac{\text{Perpendicular}}{\text{Hypotenuse}}\).
Q 2
In a right triangle, \(\cos \theta = \dfrac{\text{Perpendicular}}{\text{Base}}\).
Q 3
For an acute angle \(\tan \theta = \dfrac{\sin \theta}{\cos \theta}\).
Q 4
The reciprocal of \(\sin \theta\) is \(\sec \theta\).
Q 5
For any acute angle \(\theta?\) in a right triangle, \(\sin^2 \theta + \cos^2 \theta = 1\).
Q 6
For any acute angle \(\theta\ \sec^2 \theta - \tan^2 \theta = 1\).
Q 7
For any acute angle \(\theta\), \(\text{cosec}^2 \theta - \cot^2 \theta = 1\).
Q 8
\(\tan \theta \cdot \cot \theta = 1\) for any acute angle \(\theta\).
Q 9
\(\sin 0^\circ = 1\) and \(\cos 0^\circ = 0\).
Q 10
\(\sin 90^\circ = 1\) and \(\cos 90^\circ = 0\).
Q 11
\(\sin 30^\circ = \dfrac{1}{2}\) and \(\cos 30^\circ = \dfrac{\sqrt{3}}{2}\).
Q 12
\(\sin 45^\circ = \dfrac{1}{\sqrt{2}}\) and \(\cos 45^\circ = \dfrac{1}{\sqrt{2}}\).
Q 13
\(\tan 45^\circ = 1\)
Q 14
\(\tan 30^\circ = \sqrt{3}\) and\(\tan 60^\circ = \dfrac{1}{\sqrt{3}}\).
Q 15
\(\sin 60^\circ = \dfrac{\sqrt{3}}{2}\) and \(\cos 60^\circ = \dfrac{1}{2}\).
Q 16
For any angle \(\theta\) (where defined), \(\tan \theta = \dfrac{\sin \theta}{\cos \theta}\) and \(\cot \theta = \dfrac{\cos \theta}{\sin \theta}\).
Q 17
For complementary angles, \(\sin (90^\circ - \theta) = \cos \theta\).
Q 18
For complementary angles, \(\tan (90^\circ - \theta) = \tan \theta\).
Q 19
For complementary angles, \(\\text{cosec } (90^\circ - \theta) = \sec \theta\) and \(\cot (90^\circ - \theta) = \tan \theta\).
Q 20
In a right triangle, the hypotenuse is always the longest side.
Q 21
In a right triangle, for an acute angle \(\theta\), \(\sin \theta\) can be greater than 1.
Q 22
If sin?\(\sin \theta = \dfrac{3}{5}\) for an acute angle ?\theta?, then cos?\(\cos \theta = \dfrac{4}{5}\).
Q 23
If \(\cos \theta = \dfrac{5}{13}\) for an acute angle \(\theta\), then \(\sin \theta = \dfrac{12}{13}\).
Q 24
The trigonometric ratios introduced in Class 10 Chapter 8 are defined only for acute angles of a right triangle.
Q 25
In Class 10, the standard angles for which exact trig values are usually memorised are \(0^\circ, 30^\circ, 45^\circ, 60^\circ, 90^\circ\).
Key Takeaways — INTRODUCTION TO TRIGONOMETRY
Core facts for CBSE Boards & exams
1
sinθ = Opposite/Hypotenuse; cosθ = Adjacent/Hypotenuse; tanθ = Opposite/Adjacent.
2
sin²θ + cos²θ = 1; 1 + tan²θ = sec²θ; 1 + cot²θ = cosec²θ.
3
sin 30° = ½; sin 45° = 1/√2; sin 60° = √3/2; sin 90° = 1.
4
cosθ = sin(90°−θ); tanθ = cot(90°−θ) — complementary angle relations.
5
tan 90° is UNDEFINED; sin 0° = 0; cos 0° = 1.
6
cosecθ = 1/sinθ; secθ = 1/cosθ; cotθ = 1/tanθ.