Sketch the graphs of the following functions:
Question:

Sketch the graphs of the following functions:

(i) f(x) = 2 sin x, 0 ≤ x ≤ π

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

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

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

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

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

(vii) $u(x)=\sin ^{2} x, 0 \leq x \leq 2 \pi v(x)=|\sin x|, 0 \leq x \leq 2 \pi$

(viii) $f(x)=2 \sin \pi x, 0 \leq x \leq 2$

Solution:

The graphs of the following functions are:

(i) f(x) = 2 sin x, 0 ≤ x ≤ π

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

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

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

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

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

(vii) $u(x)=\sin ^{2} x, 0 \leq x \leq 2 \pi$

$v(x)=|\sin x|, 0 \leq x \leq 2 \pi$

(viii) $f(x)=2 \sin \pi x, 0 \leq x \leq 2$

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