Chapter 9: Trigonometric Functions-MCQs | National Book Foundation

Chapter 9: Trigonometric Functions – MCQs Test (Federal Board, National Book Foundation)

Get ready to master Chapter 9: Trigonometric Functions with this exclusive MCQs test designed specifically for 1st-year Federal Board students. These questions are based on the National Book Foundation syllabus and focus on key concepts such as domain & range of trigonometric functions, graphs, fundamental properties, and applications.

Chapter 9: Trigonometric Functions | National Book Foundation

February 21, 2025

Name

Class

The Period of $\csc {10x}$ is:

$\frac{2\pi}{5}$

$\frac{\pi}{10}$

$\frac{4\pi}{5}$

$\frac{\pi}{5}$

None

If $f(x)=\sin{8x}$ is a periodic function and its period equals:

$2\pi$

$\frac{\pi}{4}$

$\frac{\pi}{2}$

$\pi$

None

Period of $\cot (\frac{x}{2})$ is

$4\pi$

$\frac{5\pi}{2}$

$\pi$

$2\pi$

None

Range of $y=3\sin{2x}$ is

$[-6,6]$

$[-3,3]$

$[-5,5]$

$[-1,1]$

None

The smallest positive number $P$ for which $f(x+P)=f(x)$ is called:

Domain

Co-domain

Period

Range

None

$\pi$ is the period of

$\csc{2x}$

$\sin{x}$

$\cot{x}$

$\cos{x}$

None

Whether the function $f(x)=\frac{\sin^3{x}}{x^2 +\tan{x}}$ is:

Both even and Odd

Even

Neither even nor Odd

Odd

None

Range of $y=\sec {x}$ is __________

$[-1,+1]$

$y \leq-1, y \geq 1$

$y \leq-1, y \leq 1$

$[0,\pi]$

None

The trigonometric functions $y=\csc {x}$ meet at $x=$_______.

$60^{\circ}$

$120^{\circ}$

$30^{\circ}$

$90^{\circ}$

None

If $\sin(\theta +270^{\circ})=x$ and the terminal side of an angle '$\theta$' is in IV quadrant, then $x=$__________.

$\cos{\theta}$

$-\sin{\theta}$

$\sin{\theta}$

$-\cos{\theta}$

None

The exact value of trigonometric function $\tan ({-15\pi})=$_________.

Undefined

$-1$

None

If the range of the function $f(\theta)=a\sin({2\theta})+b$, where $a>0$, is$[3,5]$, then $3a+2b=$_________.

None

The period of $\cos {\frac{x}{5}}$ is:

$2\pi$

$\frac{2\pi}{5}$

$4\pi$

$10\pi$

None

The maximum value of $7\cos{x} + 24\sin{x}$ is:

$-25$

None

The range of the function $y=\cot {x}$ is

$-1\leq y \, or \, y\geq 1$

$-1\leq y \leq 1$

$\mathbb{R} : \{x \neq \,n\pi:n \in z\}$

$\mathbb{R}$

None

Period of $\tan (\frac{x}{7})$ is

$\pi$

$\frac{\pi}{7}$

$\pi+7$

$7\pi$

None

The trigonometric functions which are even and having period $2\pi$ are

$\tan{x} \,$ and $\cot {x}$

$\sin{x} \,$ and $\csc {x}$

$\sin{x} \,$ and $\cos {x}$

$\sec{x} \,$ and $ \cos {x}$

None

The graph of the _________ function from $-\pi$ to $\pi$ is:

$\cos {x}$

$\csc {x}$

$\tan {x}$

$\sin {x}$

None

If $ 2\sin {\theta} + \frac{1}{2} \csc{\theta}$ and $\theta=45^{\circ}$, then the value of the given trigonometric identity is:

$\frac{3}{\sqrt{2}}$

$\frac{2}{\sqrt{2}}$

$\frac{1}{\sqrt{2}}$

$\frac{\sqrt{2}}{3}$

None

The domain of tangent function is ______

$\mathbb{R}-\{x|x \in Z, x=(2n+1)\frac{\pi}{2}\}$

$\mathbb{R}$

$(-1,1)$

$\mathbb{R}-\{x|x \in Z, x=n\pi\}$

None

The minimum value of the trigonometric function $f(\theta)=17\sin{4\theta}$ is:

$-17$

$17$

$-4$

None

The domain of $\cot {x}$

$(\frac{-\pi}{2}, \frac{\pi}{2})$

$x \in \mathbb {R}$ but $x\neq n\pi$

$[-1,1]$

$\mathbb{Q}$

None

Trigonometric functions are _______

not periodic

discontinuous

no circular function

periodic

None

The period of $\sin {\frac{x}{2}}$ is

$2\pi$

$4\pi$

$\pi$

$\frac{\pi}{2}$

None

The trigonometric identity $\frac{\sin{\alpha}+\sin{2\alpha}}{1+\cos{\alpha}+\cos{2\alpha}}=$_______.

$\cot{\alpha}$

$\cos{\alpha}$

$\sin{\alpha}$

$\tan{\alpha}$

None

If $\cos {\theta}=-\frac{\sqrt{3}}{2}$ and the terminal arm of angles in III quadrant. Then $\sin {\theta}=$_____.

$-\frac{1}{2}$

$\frac{1}{2}$

$\frac{-2}{\sqrt{3}}$

$\sqrt{3}$

None

If $'f'$ is a periodic function and its period is $\pi$ then $f(\theta)$ could be equal to:

$2\cos {x}$

$3\cos {2x}$

$2\cos {3x}$

$\cos {4x}$

None

The range of $\cos {x}$

$-1\leq y \leq1$

$\mathbb{R}$

none of these

$y \geq 1$ or $y \leq -1$

None

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Chapter 9: Trigonometric Functions – MCQs Test (Federal Board, National Book Foundation)

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