Question 1:

\displaystyle \text{i) } f(x) = \cos \Big(  x -  \frac{\pi}{4}  \Big) \hspace{1.0cm}  \text{ii) } f(x) = \cos \Big(  x +  \frac{\pi}{4}  \Big) \hspace{1.0cm}  \text{iii) } f(x) = \cos^2 x

\displaystyle \text{iv) }\text{ } f(x) = 2 \cos \Big(  x -  \frac{\pi}{6}  \Big) \hspace{1.0cm}  \text{v) } f(x) = \cos 3x \hspace{1.0cm}  \text{vi) } f(x) = \cos^2  \frac{x}{2}

\displaystyle \text{vii) } f(x) = \cos \pi x \hspace{1.0cm}  \text{viii) } f(x) = \cos 2\pi x

Answer:

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

61

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

62

\displaystyle \text{iii) } f(x) = \cos^2 x

63

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

64

\displaystyle \text{v) } f(x) = \cos 3x

65

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

66

\displaystyle \text{vii) } f(x) = \cos \pi x

67

\displaystyle \text{viii) } f(x) = \cos 2\pi x

68

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Question 2:

\displaystyle \text{i) } y = \cos x \text{ and }  y = \cos \Big(  x -  \frac{\pi}{4}  \Big) \hspace{1.0cm} \text{ ii) } y = \cos 2x \text{ and }  y = \cos 2\Big(  x -  \frac{\pi}{4}  \Big)

\displaystyle \text{iii) } y = \cos x \text{ and }  y = \cos  \frac{x}{2} \hspace{1.0cm} \text{ iv) } y = \cos^2 x \text{ and }  y = \cos x  

Answer:

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

621

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

622

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

623

\displaystyle \text{iv) } y = \cos^2 x \text{ and } y = \cos x

624

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