Class 11: Graphs of Trigonometric Functions – Exercise 6.2 – ICSE / ISC / CBSE Mathematics Portal for K12 Students

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:

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

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

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

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

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

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

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

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

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Question 2:

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