Class 11 • Maths • Chapter 3
TRIGONOMETRIC FUNCTIONS
True & False Quiz
Oscillate. Amplify. Repeat.
✓True
✗False
25
Questions
|
Ch.3
Chapter
|
XI
Class
Why True & False for TRIGONOMETRIC FUNCTIONS?
How this format sharpens your conceptual clarity
🔵 Trigonometry is the mathematics of waves, oscillations and rotations — used in physics, engineering and signals.
✅ T/F questions test periodicity, quadrant signs, and compound angle formulas — all frequent CBSE Board question types.
🎯 Watch signs: cos(−θ)=cosθ (TRUE); sin(−θ)=−sinθ (TRUE, odd function).
📋
Read each statement carefully. Click True or False — instant feedback with explanation appears. Submit anytime; unattempted questions are marked Skipped.
Q 1
The sine of an acute angle is always positive.
Q 2
\(\cos 0^\circ = 0\).
Q 3
The value of \(\tan 45^\circ\) is equal to 1.
Q 4
\(\sin 30^\circ = \cos 60^\circ\).
Q 5
The value of \(\sec \theta\) is undefined when \(\cos \theta = 0\).
Q 6
\(\sin(-\theta) = \sin\theta\).
Q 7
\(\cos(-\theta)=\cos\theta\).
Q 8
\(\tan\theta = \frac{\sin\theta}{\cos\theta}\) for all real \(\theta\).
Q 9
The period of \(\sin x\) is \(2\pi\).
Q 10
\(\sin(\pi-\theta)=\sin\theta\).
Q 11
\(\cos(\pi-\theta)=-\cos\theta\).
Q 12
\(\tan(\pi+\theta)=\tan\theta\).
Q 13
\(\sin^2\theta+\cos^2\theta=1\) holds for all real \(\theta\).
Q 14
\(\text{cosec}^2\,\theta-\cot^2\theta=1\).
Q 15
\(\sec^2\theta-\tan^2\theta=1\).
Q 16
\(\sin 2\theta = 2\sin\theta\cos\theta\).
Q 17
\(\cos 2\theta = 1-2\sin^2\theta\) is an identity.
Q 18
\(\tan 2\theta = \frac{2\tan\theta}{1-\tan^2\theta}\) for all \(\theta\).
Q 19
The domain of \(\tan x\) excludes odd multiples of \(\frac{\pi}{2}\).
Q 20
\(\sin x\) is a one–one function on \([0,2\pi]\).
Q 21
The principal value of \(\sin^{-1}x\) lies in \(\left[-\frac{\pi}{2},\frac{\pi}{2}\right]\).
Q 22
\(\cos^{-1}(-x)=\pi-\cos^{-1}x) for (x\in[-1,1]\).
Q 23
\(\tan^{-1}x\) is defined for all real \(x\).
Q 24
If \(\sin\theta=\frac{3}{5}\) and \(\theta\) lies in the first quadrant, then \(\cos\theta=\frac{4}{5}\).
Q 25
The function \(f(x)=\sin x\) is invertible over \(\mathbb{R}\).
Key Takeaways — TRIGONOMETRIC FUNCTIONS
Core facts for CBSE Boards & JEE
1
sin²θ + cos²θ = 1 — the fundamental Pythagorean identity, always true.
2
Period of sin x and cos x = 2π; period of tan x and cot x = π.
3
sin(−θ) = −sinθ (odd); cos(−θ) = cosθ (even).
4
Range of sin x and cos x = [−1,1]; tan x has range ℝ.
5
sin(A+B) = sinA cosB + cosA sinB — signs matter in subtraction form.
6
cos 2θ has three forms: cos²θ−sin²θ = 1−2sin²θ = 2cos²θ−1.