Since, \[f\text{ }\left( x \right)\text{ }=\text{ }tan\text{ }x\]is a periodic function with period \[\pi .\] Therefore, \[f\text{ }\left( x \right)\text{ }=\text{ }ta{{n}^{2}}~\left( x \right)\]is...
Sketch the graph of the following function: f (x) = 2 sec πx
Since, \[f\text{ }\left( x \right)\text{ }=\text{ }sec\text{ }x\] is a periodic function with period \[\pi .\] Therefore, \[f\text{ }\left( x \right)\text{ }=\text{ }2\text{ }sec\text{ }\left( \pi x...
Sketch the graph of the following function: f (x) = cot 2x
Since, \[f\text{ }\left( x \right)\text{ }=\text{ }cot\text{ }x\] is a periodic function with period \[\pi .\] Therefore, \[f\text{ }\left( x \right)\text{ }=\text{ }cot\text{ }\left( 2x \right)\]...
Sketch the graphs of the following functions: f (x) = 3 sec x
Since, \[f\text{ }\left( x \right)\text{ }=\text{ }sec\text{ }x\] is a periodic function with period \[\pi .\] Therefore, \[f\text{ }\left( x \right)\text{ }=\text{ }3\text{ }sec\text{ }\left( x...
Sketch the graphs of the following functions: f (x) = 2 cosec πx
Since, \[f\text{ }\left( x \right)\text{ }=\text{ }cosec\text{ }x\]is a periodic function with period \[2\pi .\] Therefore, \[f\text{ }\left( x \right)\text{ }=\text{ }2\text{ }cosec\text{ }\left(...
Sketch the graphs of the following curves on the same scale and the same axes: (i) y = cos x and y = cos x/2 (ii) y = cos2 x and y = cos x
\[\left( \mathbf{i} \right)~y\text{ }=\text{ }cos\text{ }x\text{ }and\text{ }y\text{ }=\text{ }cos\text{ }x/2\] Since, the functions \[y\text{ }=\text{ }cos\text{ }x\text{ }and\text{ }y\text{...
Sketch the graphs of the following curves on the same scale and the same axes: (i) y = cos x and y = cos (x – π/4) (ii) y = cos 2x and y = cos (x – π/4)
\[\left( \mathbf{i} \right)~y\text{ }=\text{ }cos\text{ }x\text{ }and\text{ }y\text{ }=\text{ }cos\text{ }\left( x\text{ }-\text{ }\pi /4 \right)~\] Since, the functions \[y\text{ }=\text{...
Sketch the graphs of the following trigonometric functions: (i) f (x) = cos πx (ii) g (x) = cos 2π x
\[\left( \mathbf{i} \right)~f\text{ }\left( x \right)\text{ }=\text{ }cos\text{ }(\pi x)\] Since, \[g\text{ }\left( x \right)\text{ }=\text{ }cos\text{ }x\]is a periodic function with period \[2\pi...
Sketch the graphs of the following trigonometric functions: (i) ψ (x) = cos (3x) (ii) u (x) = cos2 x/2
\[\left( \mathbf{i} \right)~\psi \text{ }\left( x \right)\text{ }=\text{ }cos\text{ }\left( 3x \right)\] Since, \[f\text{ }\left( x \right)\text{ }=\text{ }cos\text{ }x\] is a periodic function with...
Sketch the graphs of the following trigonometric functions: (i) h (x) = cos^2 2x (ii) ϕ (x) = 2 cos (x – π/6)
\[\left( \mathbf{i} \right)~h\text{ }\left( x \right)\text{ }=\text{ }co{{s}^{2}}~2x\] Since, \[f\text{ }\left( x \right)\text{ }=\text{ }cos\text{ }x\]is a periodic function with period \[2\pi .\]...
Sketch the graphs of the following trigonometric functions: (i) f (x) = cos (x – π/4) (ii) g (x) = cos (x + π/4)
\[\left( \mathbf{i} \right)~f\text{ }\left( x \right)\text{ }=\text{ }cos\text{ }\left( x\text{ }-\text{ }\pi /4 \right)\] Since, \[g\text{ }\left( x \right)\text{ }=\text{ }cos\text{ }x\]is a...
Sketch the graphs of the following pairs of functions on the same axes: (i) f (x) = sin 2x, g (x) = 2 sin x (ii) f (x) = sin x/2, g (x) = sin x
\[\left( \mathbf{i} \right)~f\text{ }\left( x \right)\text{ }=\text{ }sin\text{ }(2x),\text{ }g\text{ }\left( x \right)\text{ }=\text{ }2\text{ }sin\text{ }x\] Since, the functions \[f\left( x...
Sketch the graphs of the following pairs of functions on the same axes: (i) f (x) = sin x, g (x) = sin (x + π/4) (ii) f (x) = sin x, g (x) = sin 2x
\[\left( \mathbf{i} \right)~f\text{ }\left( x \right)\text{ }=\text{ }sin\text{ }x,\text{ }g\text{ }\left( x \right)\text{ }=\text{ }sin\text{ }\left( x\text{ }+\text{ }\pi /4 \right)\] Since, the...
Sketch the graphs of the following functions: (i) u (x) = sin2 x, 0 ≤ x ≤ 2π υ (x) = |sin x|, 0 ≤ x ≤ 2π (ii) f (x) = 2 sin πx, 0 ≤ x ≤ 2
\[\left( \mathbf{i} \right)~u\text{ }\left( x \right)\text{ }=\text{ }si{{n}^{2}}~x,\text{ }0\text{ }\le \text{ }x\text{ }\le \text{ }2\pi \text{ }\upsilon \text{ }\left( x \right)\text{ }=\text{...
Sketch the graphs of the following functions: (i) Ψ (x) = 4 sin 3 (x – π/4), 0 ≤ x ≤ 2π (ii) θ (x) = sin (x/2 – π/4), 0 ≤ x ≤ 4π
\[\left( \mathbf{i} \right)~\Psi \text{ }\left( x \right)\text{ }=\text{ }4\text{ }sin\text{ }3\text{ }\left( x\text{ }-\text{ }\pi /4 \right),\text{ }0\text{ }\le \text{ }x\text{ }\le \text{ }2\pi...
Sketch the graphs of the following functions: (i) h (x) = 2 sin 3x, 0 ≤ x ≤ 2π/3 (ii) ϕ (x) = 2 sin (2x – π/3), 0 ≤ x ≤ 7π/3
\[\left( \mathbf{i} \right)~h\text{ }\left( x \right)\text{ }=\text{ }2\text{ }sin\text{ }3x,\text{ }0\text{ }\le \text{ }x\text{ }\le \text{ }2\pi /3\] Since, \[g\text{ }\left( x \right)\text{...
Sketch the graphs of the following functions: (i) f (x) = 2 sin x, 0 ≤ x ≤ π (ii) g (x) = 3 sin (x – π/4), 0 ≤ x ≤ 5π/4
\[\left( \mathbf{i} \right)~f\text{ }\left( x \right)\text{ }=\text{ }2\text{ }(sin\text{ }x),\text{ }0\text{ }\le \text{ }(x)\text{ }\le \text{ }\pi \] Since, \[g\text{ }\left( x \right)\text{...