Question

Sketch the graphs of the following functions:

(i) f(x) = 2 sin x, 0 ≤ x ≤ π
(ii) $g\left(x\right)=3\sin \left(x-\frac{\pi }{4}\right),0\le x\le \frac{5\pi }{4}$
(iii) $h\left(x\right)=2\sin 3x,0\le x\le \frac{2\pi }{3}$
(iv) $\mathrm{\varphi }\left(x\right)=2\sin \left(2x-\frac{\pi }{3}\right),0\le x\le \frac{7\pi }{5}$
(v) $\mathrm{\psi }\left(x\right)=4\sin 3\left(x-\frac{\pi }{4}\right),0\le x\le 2\pi$
(vi) $\mathrm{\theta }\left(x\right)=\sin \left(\frac{x}{2}-\frac{\pi }{4}\right),0\le x\le 4\pi$
(vii) $u\left(x\right)={\sin }^{2}x,0\le x\le 2\pi v\left(x\right)=\left|\sin x\right|,0\le x\le 2\pi$
(viii) f(x) = 2 sin πx, 0 ≤ x ≤ 2

Answer 1

The graphs of the following functions are:

(i) f(x) = 2 sin x, 0 ≤ x ≤ π

x	0	π
f(x) = 2 sin x	0	0

(ii) $g\left(x\right)=3\sin \left(x-\frac{\pi }{4}\right),0\le x\le \frac{5\pi }{4}$

x	$\frac{\mathrm{\pi }}{4}$	$\frac{5\mathrm{\pi }}{4}$
$g\left(x\right)=3\sin \left(x-\frac{\pi }{4}\right)$	0	0

(iii) $h\left(x\right)=2\sin 3x,0\le x\le \frac{2\pi }{3}$

x	0	$\frac{\mathrm{\pi }}{3}$	$\frac{2\mathrm{\pi }}{3}$
$h\left(x\right)=2\sin 3x$	0	0	0

(iv) $\mathrm{\varphi }\left(x\right)=2\sin \left(2x-\frac{\pi }{3}\right),0\le x\le \frac{7\pi }{5}$

x	$\frac{\mathrm{\pi }}{6}$	$\frac{4\mathrm{\pi }}{6}$
$\mathrm{\varphi }\left(x\right)=2\sin \left(2x-\frac{\pi }{3}\right)$	0	0

(v) $\mathrm{\psi }\left(x\right)=4\sin 3\left(x-\frac{\pi }{4}\right),0\le x\le 2\pi$

x	$\frac{\mathrm{\pi }}{4}$	$\frac{7\mathrm{\pi }}{12}$
$\mathrm{\psi }\left(x\right)=4\sin 3\left(x-\frac{\pi }{4}\right)$	0	0

(vi) $\mathrm{\theta }\left(x\right)=\sin \left(\frac{x}{2}-\frac{\pi }{4}\right),0\le x\le 4\pi$

x	$\frac{\mathrm{\pi }}{2}$	$\frac{5\mathrm{\pi }}{2}$
$\mathrm{\theta }\left(x\right)=\sin \left(\frac{x}{2}-\frac{\pi }{4}\right)$	0	0

(vii) $$\begin{gathered} u\left(x\right)={\sin }^{2}x,0\le x\le 2\mathrm{\pi } \\ v\left(x\right)=\left|\sin x\right|,0\le x\le 2\mathrm{\pi } \end{gathered}$$

x	0	$\mathrm{\pi }$
$u\left(x\right)={\sin }^{2}x$	0	0

x	0	$\mathrm{\pi }$
$v\left(x\right)=\left|\sin x\right|$	0	0

(viii) f(x) = 2 sin πx, 0 ≤ x ≤ 2

x	0	1
f(x) = 2 sin πx	0	0