Unit-I: Sets and Functions
Unit-II: Algebra
Unit-III: Coordinate Geometry
Unit-IV: Calculus
Unit-V: Mathematical Reasoning
Unit-VI: Statistics and Probability

Graphs of Trigonometric Functions

(i)  Graph of  y =\sin x

We take the interval [-\pi, \pi] , where length of the interval is  2 \pi .

(i) For  - \pi  \leq x \leq -\dfrac{\pi}{2}, \sin x decreases from  0 \text { to } -1.

(ii) For -\dfrac{\pi}{2} \leq x \leq 0 ,  \sin x increases from  -1 \text { to } 0 .

(iii) For 0 \leq x \leq \dfrac{\pi}{2} ,  \sin x increases from  0\text { to } 1 .

(iv) For \dfrac{\pi}{2} \leq x \leq \pi , \sin x decrease from  1 \text { to } 0.

 | \sin x |  \leq 1 i.e.  -1 \leq \sin x \leq 1 , its graph lies between the lines y=-1   and  y=1 .

 y=\sin x

(ii) Graph of  y= \cos x

In interval [- \pi, \pi]

(i) For  - \pi < x \leq 0 ,  \cos x increases from -1 \text { to } 1

(ii) For  0 \leq x \leq \pi, decreases from  1 \text { to } -1

 \cos x =0 at  x=-\dfrac{\pi}{2} and \dfrac{\pi}{2}

 |\cos x| \leq 1,  -1 \leq \cos x \leq 1.

This graph lies between  y=-1  and  y=1 .

 y=\cos x

(iii) Graph of  y=\tan x

\tan x is not defined at  -\dfrac{\pi}{2} and  \dfrac{\pi}{2} . It increases from  -\infty to  0 in  \left(-\dfrac{\pi}{2}, 0 \right] and then from  0 to  \infty in \left[0, \dfrac{\pi}{2} \right) .

y= \tan x

(iv) Graph of  y=\cot x

 \cot x is not defined at 0, \pi and -\pi . So, the graph of y=\cot x is  a decreasing graph.

y=\cot x

(v) Graph of  y=\sec x

(i)  \sec x decreases from  -1 \text { to } -\infty in \left[ -\pi, -\dfrac{\pi}{2} \right) and is undefined at  x=-\dfrac{\pi}{2} .

(ii) It again decreases from  \infty \text { to } 1 in  \left( -\dfrac{\pi}{2},0 \right] and increases from  1 \text { to } \infty in  \left[ 0, \dfrac{\pi}{2} \right) and is undefined at  x=\dfrac{\pi}{2}

(iii) It increases from -\infty \text { to } -1 in  \left( \dfrac{\pi}{2}, \pi \right].

y=\sec x

(vi) Graph of  y=\csc x

(i) \csc x is undefined at  x=- \pi. It increases from  -\infty \text { to } -1 in the interval  \left(-\pi, -\dfrac{\pi}{2} \right].

(ii) It decreases from  -1 \text { to } -\infty in  \left[ -\dfrac{\pi}{2}, 0 \right) and is undefined at  x=0.

(iii) It decreases from  \infty \text { to } 1 in \left( 0, \dfrac{\pi}{2} \right] and again increases from 1 \text { to } \infty   in  \left[ \dfrac{\pi}{2}, \pi \right) and is undefined at x=\pi .

y=\csc x
Scroll to Top