Question 1,Review Exercise
Solutions of Question 1 of Review Exercise of Unit 09: Trigonometric Functions. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan.
Select the best matching option.
Chose the correct option.
i. If $\cos \theta=\frac{\sqrt{3}}{2}$ and the terminal arm of angle is in III quadrant. Then $\sin \theta=$
- $\frac{1}{2}$
- (b) $-\frac{1}{2}$
- (c) $\sqrt{3}$
- (d) $-\frac{2}{\sqrt{3}}$
<btn type=“link” collapse=“a1”>See Answer</btn>(b): $-\frac{1}{2}$
ii. The exact value of the trigonometric function $\tan (-15 \pi)=$
* (a) $ 0$
* (b) $-1$
* (c) $1$
* (d) undefined
<btn type=“link” collapse=“a2”>See Answer</btn>
(a): $0$
iii. If $2 \sin \theta+\frac{1}{2}cosec \theta \theta $ and $\theta=45^{\circ}$, then the value of the given trigonometric identity is:
* (a) $\frac{1}{\sqrt{2}}$
* (b)$\frac{1}{3}$
* (c) $\frac{3}{\sqrt{2}}$
* (d) $\frac{\sqrt{2}}{3}$
<btn type=“link” collapse=“a3”>See Answer</btn>
©: $\frac{3}{\sqrt{2}}$
iv. If $\sin (270^{\circ}+\theta)=x$ and the terminal side of an angle $'\theta'$ is in IV quadrant, then $x=$
* (a) $\cos \theta$
* (b) $-\cos \theta$
* (c) $\sin \theta$
* (d) $-\sin \theta$
<btn type=“link” collapse=“a4”>See Answer</btn>
(a):$\cos \theta$
v. The trigonometric identity $\dfrac{\sin \alpha + \sin 2\alpha}{1+ \cos \alpha+\cos 2\alpha}=$
* (a) $\sin \alpha$
* (b) $\cos \alpha$
* (c) $\tan \alpha$
* (d) $\cot \alpha$
<btn type=“link” collapse=“a5”>See Answer</btn>
©: $\tan \alpha$
vi. Express $2\sin 3x \sin 7x$ as a sum or difference:
* (a) $\cos 4x-\cos 10x$
* (b) $\cos 10x-\cos 4x$
* (c) $\cos 4x+\cos 10x$
* (d) $\cos 10x+\cos 4x$
<btn type=“link” collapse=“a6”>See Answer</btn>
(a): $\cos 4x-\cos 10x$
vii. Express $\sin 5x+\sin 7x$ as a product:
* (a) $2\sin 6x \cos x$
* (b) $2\sin x \cos 6x$
* (c) $2\cos 7x \sin 5x$
* (d) $2\cos 5x \sin 7x$
<btn type=“link” collapse=“a7”>See Answer</btn>
(a): $2\sin 6x \cos x$
viii. The value of $\tan x \cdot \tan(\dfrac{\pi}{3}-x)\cdot \tan(\dfrac{\pi}{3}+x) $ is:
* (a) $2\cot 3x$
* (b) $\cot 3x$
* (c) $3\tan 3x$
* (d) $\tan 3x$
<btn type=“link” collapse=“a8”>See Answer</btn>
(d): $\tan 3x$
ix. If $\tan A=\frac{1}{7}$ and $\tan B=\frac{1}{3}$, then $\cos 2A$ is equal to:
* (a) $\sin B$
* (b) $\sin 4B$
* (c) $\sin 3B$
* (d) $\sin 2B$
<btn type=“link” collapse=“a9”>See Answer</btn>
(b): $\sin 4B$
x. Whether the function $f(x)=\frac{\sin^3 x}{x^2+\tan x}$ is:
* (a) even
* (b) odd
* (c) neither even nor odd
* (d) both even and odd
<btn type=“link” collapse=“a10”>See Answer</btn>
(c): neither even nor odd
xi. The period of $\cos \frac{x}{5}$ is:
* (a) $10 \pi$
* (b) $\frac{2\pi}{5}$
* (c) $2\pi$
* (d) $4 \pi$
<btn type=“link” collapse=“a11”>See Answer</btn>
(a): $10 \pi$
xii. The trogonometric function $y=cosec x$ meet at $x=$
* (a) $30^{\circ}$ \
* (b) $60^{\circ}$
* (c) $90^{\circ}$
* (d) $120^{\circ}$
<btn type=“link” collapse=“a12”>See Answer</btn>
(c): $90^{\circ}$
xiii. $2\cos 5x \cdot \sin 3x=$
* (a) $\sin 8x+\sin 2x$
* (b) $\sin 8x-\sin 2x$
* (c) $\cos 8x+\cos 2x$
* (d) $\sin 4x-\sin x$
<btn type=“link” collapse=“a13”>See Answer</btn>
(a): $\sin 8x+\sin 2x$
xiv. The trigonometric functions, which are even and having period $=2\pi$ are
* (a) $\sin x$ & $\cos x$
* (b) $\sec x$ & $ \cos x$
* (c) $\sin x $ & $ cosec x$
* (d) $\tan x $ & $\cot x$
<btn type=“link” collapse=“a14”>See Answer</btn>
(b): $\sec x$ & $ \cos x$
xv. If $'f'$ is periodic function and its period is $\pi$, then $f(\theta)$ could be equal to:
* (a) $2\cos x$
* (b) $2 \cos 3x$
* (c) $3\cos2x$
* (d) $\cos 4 x$
<btn type=“link” collapse=“a15”>See Answer</btn>
(c): $3\cos2x$
xvi. If function $f(x)=\sin 8x$ is a periodic function and its period equals:
* (a) $\pi$
* (b) $\frac{\pi}{4}$
* (c) $2\pi$
* (d) $\frac{\pi}{2}$
<btn type=“link” collapse=“a16”>See Answer</btn>
(b): $\frac{\pi}{4}$
xvii. If the range of the function $f(0)=a \sin (2\theta)+b$, where $a>0$, is \{3,5\}, then $3a+2b=$
* (a) $11$
* (b) $14$
* (c) $9$
* (d) $5$
<btn type=“link” collapse=“a17”>See Answer</btn>
(a): $11$
xviii. The minimum value of the trigonometric function $f(0)=17 \sin(4\theta)$ is :
* (a) $4$
* (b) $-4$
* (c) $-17$
* (d) $17$
<btn type=“link” collapse=“a18”>See Answer</btn>
(c): $-17$
xix. If the given figure represent the curve $y=3\sin x$, then $|a|+|b|=$ FixMe
* (a) $1$
* (b) $2$
* (c) $3$
* (d) $6$
<btn type=“link” collapse=“a19”>See Answer</btn>
(d): $6$
xx. The minimum value of $7 \cos x+24 \sin x$ is:
* (a) $25$
* (b) $-25$
* (c) $7$
* (d) $24$
<btn type=“link” collapse=“a20”>See Answer</btn>
(a): $25$
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