Sketch the following graphs-i y-cos x- 4ii y-cos x- 4iii y-3 cos 2 x-1iv y-2 cos x- 2

(i) y=cosx+π4⇒ nbsp;y 0=cosx+π4 nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp ...

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Byju's Answer

Standard X

Mathematics

Linear Equations in Two Variables

Sketch the fo...

Question

Sketch the following graphs:

(i) $y = \cos (x + \frac{π}{4})$
(ii) $y = \cos (x - \frac{π}{4})$
(iii) y = 3 cos (2x − 1)
(iv) $y = 2 \cos (x - \frac{π}{2})$

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Solution

(i)
$y = \cos (x + \frac{π}{4}) \Rightarrow y - 0 = \cos (x + \frac{π}{4}) . . . (i) O n shifting the origin at (- \frac{π}{4}, 0), we g e t : x = X - \frac{π}{4} and y = Y + 0 On subsitituting the values in (i), we get : Y = \cos X Then, we draw the graph of Y = \cos X and shift it by \frac{π}{4} to the left .$
Then, we obtain the following graph:

(ii)
$y = \cos (x - \frac{π}{4}) \Rightarrow y - 0 = \cos (x - \frac{π}{4}) . . . (i) O n shifting the origin at (\frac{π}{4}, 0), we g e t : x = X + \frac{π}{4} and y = Y + 0 O n subsititut i n g the values in (i) we get : Y = \cos X Then, we draw the graph of Y = \cos X and shift it by \frac{π}{4} to the right .$
Then, we obtain the following graph:

(iii)
$y = 3 \cos (2 x - 1) \Rightarrow y - 0 = 3 \cos 2 (x - \frac{1}{2}) . . . (i) O n shifting the origin at (\frac{1}{2}, 0), we have : x = X + \frac{1}{2} and y = Y + 0 O n subsititut i n g the values in (i), we get : Y = 3 \cos 2 X Then, we draw the graph of Y = 3 \cos 2 X and shift it by \frac{1}{2} to the right .$
Then, we obtain the following graph:

(iv)
$y = 2 \cos (x - \frac{π}{2}) \Rightarrow y - 0 = 2 \cos (x - \frac{π}{2}) . . . (i) O n shifting the origin at (\frac{π}{2}, 0), we g e t : x = X + \frac{π}{2} and y = Y + 0 O n subsititut i n g the values in (i), we get : Y = 2 \cos X Then, we draw the graph of Y = \cos X and shift it by \frac{π}{2} to the right .$
Then, we obtain the following graph:

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Similar questions

Sketch the following graphs :
(i) $y = c o s (x + \frac{π}{4})$
(ii) $y = c o s (x - \frac{π}{4})$
(iii) $y = 3 c o s (2 x - 1)$
(iv) $y = 2 c o s (x - \frac{π}{2})$

Q. Sketch the graphs of the following functions on the same scale.

(i)

y = \cos x and y = \cos (x - \frac{π}{4})

(ii)

y = \cos 2 x and y = \cos 2 (x - \frac{π}{4})

(iii)

y = \cos x and y = \cos (\frac{x}{2})

Q. Sketch the graphs of the following curves on the same scale and the same axes:
(i)

y = \cos x and y = \cos (x - \frac{π}{4})

(ii)

y = \cos 2 x and y = \cos 2 (x - \frac{π}{4})

(iii)

y = \cos x and y = \cos \frac{x}{2}

(iv)

y = \cos^{2} x and y = \cos x

Q. Sketch the graphs of the following trigonometric functions:
(i)

f (x) = \cos (x - \frac{π}{4})

(ii)

g (x) = \cos (x + \frac{π}{4})

(iii) h(x) = cos² 2x
(iv)

ϕ (x) = 2 \cos (x - \frac{π}{6})

(v) ψ(x) = cos 3x
(vi)

u (x) = \cos^{2} \frac{x}{2}

(vii) f(x) = cos π x
(viii) g(x) = cos 2π x

Sketch the graph of the following functions on the same scale.
(i) y=cos x and y =cos $(x - \frac{π}{4})$
(ii) y=cos 2 x and y = cos2 $(x - \frac{π}{4})$
(iii) y =cos x and y = cos $(\frac{x}{2})$

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Sketch the following graphs: (i) y=cosx+π4 (ii) y=cosx-π4 (iii) y = 3 cos (2x − 1) (iv) y=2 cosx-π2

Sketch the following graphs:

(i) $y = \cos (x + \frac{π}{4})$
(ii) $y = \cos (x - \frac{π}{4})$
(iii) y = 3 cos (2x − 1)
(iv) $y = 2 \cos (x - \frac{π}{2})$