Question 1:

i) $f(x) = \cos \Big( x -$ $\frac{\pi}{4}$ $\Big)$    ii) $f(x) = \cos \Big( x +$ $\frac{\pi}{4}$ $\Big)$    iii) $f(x) = \cos^2 x$

iv) $f(x) = 2 \cos \Big( x -$ $\frac{\pi}{6}$ $\Big)$    v) $f(x) = \cos 3x$    vi) $f(x) = \cos^2$ $\frac{x}{2}$

vii) $f(x) = \cos \pi x$    viii) $f(x) = \cos 2\pi x$

Answer:

i) $f(x) = \cos \Big( x -$ $\frac{\pi}{4}$ $\Big)$

ii) $f(x) = \cos \Big( x +$ $\frac{\pi}{4}$ $\Big)$

iii) $f(x) = \cos^2 x$

iv) $f(x) = 2 \cos \Big( x -$ $\frac{\pi}{6}$ $\Big)$

v) $f(x) = \cos 3x$

vi) $f(x) = \cos^2$ $\frac{x}{2}$

vii) $f(x) = \cos \pi x$

viii) $f(x) = \cos 2\pi x$

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Question 2:

i) $y = \cos x$ and $y = \cos \Big( x -$ $\frac{\pi}{4}$ $\Big)$    ii) $y = \cos 2x$ and $y = \cos 2\Big( x -$ $\frac{\pi}{4}$ $\Big)$

iii) $y = \cos x$ and $y = \cos$ $\frac{x}{2}$    iv) $y = \cos^2 x$ and $y = \cos x$

Answer:

i) $y = \cos x$ and $y = \cos \Big( x -$ $\frac{\pi}{4}$ $\Big)$

ii) $y = \cos 2x$ and $y = \cos 2\Big( x -$ $\frac{\pi}{4}$ $\Big)$

iii) $y = \cos x$ and $y = \cos$ $\frac{x}{2}$

iv) $y = \cos^2 x$ and $y = \cos x$