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) $-\frac{2}{\sqrt{3}}$
    See Answer
    (b): $-\frac{1}{2}$

ii. The exact value of the trigonometric function $\tan (-15 \pi)=$
* (a) $ 0$
* (b) $-1$
* (c) $1$
* (d) undefined
See Answer

(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) $\frac{\sqrt{2}}{3}$
See Answer

©: $\frac{3}{\sqrt{2}}$

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) $-\sin \theta$
See Answer

(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) $\cot \alpha$
See Answer

©: $\tan \alpha$

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) $\cos 10x+\cos 4x$
See Answer

(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) $2\cos 5x \sin 7x$
See Answer

(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) $\tan 3x$
See Answer

(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) $\sin 2B$
See Answer

(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
See Answer

(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) $4 \pi$
See Answer

(a): $10 \pi$

xii. The trogonometric function $y=cosec x$ meet at $x=$
* (a) $30^{\circ}$ \
* (b) $60^{\circ}$
* (c) $90^{\circ}$
* (d) $120^{\circ}$
See Answer

(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) $\sin 4x-\sin x$
See Answer

(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 $ & $\cot x$
See Answer

(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) $\cos 4 x$
See Answer

(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) $\frac{\pi}{2}$
See Answer

(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) $5$
See Answer

(a): $11$

xviii. The minimum value of the trigonometric function $f(0)=17 \sin(4\theta)$ is :
* (a) $4$
* (b) $-4$
* (c) $-17$
* (d) $17$
See Answer

(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) $6$
See Answer

(d): $6$

xx. The minimum value of $7 \cos x+24 \sin x$ is:
* (a) $25$
* (b) $-25$
* (c) $7$
* (d) $24$
See Answer

(a): $25$

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