Chapter 2

Draw the graphs of $$ f(x)=1-\sin |x| $$

Draw the graphs of $$ f(x)=\operatorname{sgn}(\sin x) $$

Draw the graphs of $$ f(x)=\cos x+|\cos x| $$

Draw the graphs of $$ f(x)=\sin |x| $$

Draw the graphs of $$ f(x)=\operatorname{sgn}(\cos x) $$

Draw the graphs of $$ f(x)=\cos x-|\cos x| $$

Draw the graphs of $$ f(x)=\sin |x-1| $$

Find the maximum and minimum values of (i) \(f(x)=\sin ^{2} x+\cos ^{4} x\) (ii) \(f(x)=\sin ^{4} x+\cos ^{2} x\) (iii) \(f(x)=\sin ^{4} x+\cos ^{4} x\) (iv) \(f(x)=\sin ^{6} x+\cos ^{6} x\)

Draw the graphs of $$ f(x)=\cos x+\cos |x| $$

Draw the graphs of $$ f(x)=\sin |x+1| $$

Find the number of solutions of (i) \(2^{\sin x}=\sin x, \forall x \in[0,4 \pi]\) (ii) \(2^{\sin x}=|\sin x|, \forall x \in[0,4 \pi]\) (iii) \(2^{\cos x}=|\sin x|, \forall x \in[0,8 \pi]\) (iv) \(2^{\cos x}=|\cos x|, \forall x \in[0,10 \pi]\) (v) \(2^{\cos x}=\cos x, \forall x \in[0,20 \pi]\) (vi) \(x \sin x-1=0, \forall x \in[0,2 \pi]\) (vii) \(x \sin ^{2} x-1=0, \forall x \in[0,2 \pi]\) (viii) \(\sin x=2^{x}+2^{x}, \forall x \in[0,2 \pi]\) (ix) \(\cos x=2^{x}-2^{x}, \forall x \in[0,2 \pi]\) (x) \(x^{2} \cos x-2=0, \forall x \in[0,2 \pi]\)

Draw the graphs of $$ f(x)=\cos x-\cos |x| $$

Draw the graphs of $$ f(x)=\sin ^{2} x $$

Draw the graphs of $$ f(x)=\max \left\\{\sin x, \frac{1}{2}\right\\} $$

Draw the graphs of $$ f(x)=\sin ^{2} x-1 $$

Draw the graphs of $$ f(x)=\sin ^{2} x-1 $$

Draw the graphs of $$ f(x)=1-\sin ^{2} x $$

Draw the graphs of $$ f(x)=\max \left\\{\sin \left(x-\frac{\pi}{4}\right), \sin \left(x+\frac{\pi}{4}\right)\right\\} $$

Draw the graphs of $$ f(x)=\sin ^{2} x+\cos ^{2} x $$

Draw the graphs of $$ f(x)=\tan x+\tan |x| $$

Draw the graphs of $$ f(x)=|\sin | x \| $$

Draw the graphs of $$ f(x)=\tan x-\tan |x| $$

Draw the graphs of $$ f(x)=|\sin | x \|+1 $$

Draw the graphs of $$ f(x)=\tan x \cdot \cot x $$

Draw the graphs of $$ f(x)=|\sin | x \|-1 $$

Draw the graphs of $$ f(x)=\sin x \cdot \operatorname{cosec} x $$

Draw the graphs of $$ f(x)=\cos 2 x $$

Draw the graphs of $$ f(x)=\cos x \cdot \sec x $$

Draw the graphs of $$ f(x)=\cos 4 x $$

Draw the graphs of $$ f(x)=\cos \left(\frac{x}{2}\right) $$

Find the maximum and minimum values of (i) \(f(x)=\sin x+\cos x\) (ii) \(f(x)=\sin x-\cos x\) (iii) \(f(x)=3 \sin x+4 \cos x+10\) (iv) \(f(x)=5 \sin x+12 \cos x+12\) (v) \(f(x)=\sin (x-1)+\cos x\) (vi) \(f(x)=\sin x+\cos (x-1)\) (vii) \(f(x)=3 \sin x+4\) (viii) \(f(x)=2-4 \sin x\) (ix) \(f(x)=-3-2 \sin x\) (x) \(f(x)=3 \cos x+5\) (xi) \(f(x)=-2 \cos x+3\) (xii) \(f(x)=3 \sin ^{2} x+4\) (xiii) \(f(x)=2-4 \sin ^{2} x\) (xiv) \(f(x)=3 \sin ^{2} x+4 \cos ^{2} x\) \((\mathrm{xv}) f(x)=2 \sin ^{2} x-3 \cos ^{2} x\) (xvi) \(f(x)=3 \sin ^{2} x+4 \cos ^{2} x+10 \sin x \cos x\) (xvii) \(f(x)=\frac{1}{3 \sin ^{2} x+2 \cos ^{2} x}\) (xviii) \(f(x)=\frac{1}{3 \sin ^{2} x-2 \cos ^{2} x}\) \((\) xix \() f(x)=2^{5 \sin ^{2} x+6 \cos ^{2} x}\) \((x x) f(x)=\log _{2}\left(3 \sin ^{2} x+1\right)\)

Draw the graphs of $$ f(x)=\cos \left(\frac{x}{3}\right) $$

Find the domains and ranges of (i) \(f(x)=2 \sin x+4\) (ii) \(f(x)=\sin x+\cos x\) (iii) \(f(x)=\sin x+\cos x+1\) (iv) \(f(x)=3 \sin x+4 \cos x+10\) (v) \(f(x)=\sin \left(x-\frac{\pi}{4}\right)+\cos x\) (vi) \(f(x)=\sin \left(x-\frac{\pi}{4}\right)+\cos \left(x-\frac{\pi}{6}\right)\) (vii) \(f(x)=\sin \left(x-\frac{\pi}{4}\right)+\cos \left(x-\frac{\pi}{4}\right)\) (viii) \(f(x)=3 \sin ^{2} x+2\) (ix) \(f(x)=3 \sin ^{2} x+2 \cos ^{2} x\) (x) \(f(x)=3 \sin ^{2} x-4 \cos ^{2} x\)

Draw the graphs of $$ f(x)=-\cos x $$

Draw the graphs of $$ f(x)=1-\cos x $$

Draw the graphs of $$ f(x)=\cos \left(x-\frac{\pi}{4}\right) $$

Draw the graphs of $$ f(x)=\cos \left(x+\frac{\pi}{4}\right) $$

Draw the graphs of $$ f(x)=\cos (x-1) $$

Draw the graphs of $$ f(x)=\cos (x+1) $$

Draw the graphs of $$ f(x)=\cos \left(x-\frac{\pi}{4}\right)+1 $$

Draw the graphs of $$ f(x)=\cos \left(x+\frac{\pi}{4}\right)-1 $$

Draw the graphs of $$ f(x)=|\cos x| $$

Draw the graphs of $$ f(x)=-|\cos x| $$

Draw the graphs of $$ f(x)=1-|\cos x| $$

Draw the graphs of $$ f(x)=\|\cos x\| $$

Draw the graphs of $$ f(x)=|\cos (x-1)| $$

Draw the graphs of $$ f(x)=\cos |x| $$

Draw the graphs of $$ f(x)=\cos _{2}|x|+1 $$

Draw the graphs of $$ f(x)=\cos ^{2} x $$

Draw the graphs of $$ f(x)=\cos ^{3} x $$