Sketch the graphs of the following functions: (i) h (x) = 2 sin 3x, 0 ≤ x ≤ 2π/3 (ii) ϕ (x) = 2 sin (2x

Home » 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

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

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,

$g\text{ }\left( x \right)\text{ }=\text{ }sin\text{ }x$

is a periodic function with period

$2\pi .$

Therefore,

$h\text{ }\left( x \right)\text{ }=\text{ }2\text{ }sin\text{ }3x$

is a periodic function with period

$2\pi /3.$

Hence, we draw the graph of

$h\text{ }\left( x \right)\text{ }=\text{ }2\text{ }sin\text{ }3x$

in the interval

$\left[ 0,\text{ }2\pi /3 \right].$

The values of

$h\text{ }\left( x \right)\text{ }=\text{ }2\text{ }sin\text{ }3x$

at various points in

$\left[ 0,\text{ }2\pi /3 \right]$

are listed in below:

The curve is:

RD Sharma Solutions for Class 11 Maths Chapter 6 – Graphs of Trigonometric Functions image -3

$\left( \mathbf{ii} \right)~\phi \text{ }\left( x \right)\text{ }=\text{ }2\text{ }sin\text{ }\left( 2x\text{ }-\text{ }\pi /3 \right),\text{ }0\text{ }\le \text{ }x\text{ }\le \text{ }7\pi /3$