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Graphs of General Trigonometric Functions - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main

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  • 33 Questions around this concept.

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Range of  $f(x)=\sin|3x^3| \ \ x\epsilon R$

The number of solutions of the equation $x+2 \tan x=\frac{\pi}{2}$ in the interval $[0,2 \pi]$ is :

Which of the following can be a graph of f(x ) = $\tan 3 x ?$

$\cos x<\frac{1}{2}$ for $x$ in the interval $(0,2 \pi):$

$\cos ^{-1}\left(\frac{\sqrt{3}}{2}\right)=$

$\sin x>\frac{1}{2}$ for $x$ in the interval $(-2 \pi, 2 \pi)$ :

If $4\sin ^{2}\alpha =1,$ then the values of alpha are

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If $x=2\sin^{2}\alpha - \cos2\alpha, then \:\: x \:\: lies \:\: in\:\: the \:\: interval$

What is the solution of $cotx$ $>1$ in the interval $(0,2 \pi)$

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What is the solution set of the equation $\csc x>1$ in the interval $[0,2 \pi$ ]?

Concepts Covered - 2

Graph of Trigonometric Function (Part 1)

Graph of Trigonometric Function (Part 1)

Sine Function 

$y=f(x)=\sin (x)$

Domain is R

Range is  [-1, 1]

Cosine Function

$y=f(x)=\cos (x)$

Domain is R 

Range is [-1, 1]

Tangent Function

$y=f(x)=\tan (x)$

$\mathrm{Domain\;is\;\;\mathbb{R}-\left \{ \frac{(2n+1)\pi}{2},\;n\in\;\mathbb{I} \right \}}$

Range is R

Graph of Trigonometric Function (Part 2)

Graph of Trigonometric Function (Part 2)

Cosecant Function

$y=f(x)=\operatorname{cosec}(x)$

 

Domain is R - $\{\mathrm{n} \pi, \mathrm{n} \in \mathrm{I}$ (Integers) $\}$
Range is $\mathrm{R}-(-1,1)$
Period is $2 \pi$

Secant Function

$y=f(x)=\sec (x)$

$\mathrm{Domain\;is\;\;\mathbb{R}-\left \{ \frac{(2n+1)\pi}{2},\;n\in\;\mathbb{I} \right \}}$

The range is $\mathrm{R}-(-1,1)$
Period is $2 \pi$

Cotangent Function

$y=f(x)=\cot (x)$

 

Domain is R - $\{\mathrm{n} \pi, \mathrm{n} \in \mathrm{I}$ (Integers) $\}$
Range is $R$
Period is $2 \pi$

Study it with Videos

Graph of Trigonometric Function (Part 1)
Graph of Trigonometric Function (Part 2)

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Books

Reference Books

Graph of Trigonometric Function (Part 1)

Mathematics for Joint Entrance Examination JEE (Advanced) : Trigonometry

Page No. : 2.13

Line : 45

Graph of Trigonometric Function (Part 2)

Mathematics for Joint Entrance Examination JEE (Advanced) : Trigonometry

Page No. : 2.14

Line : 4

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