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EXAMPLE 7
Plot y = sin x and y = cos 2x for 0 £ x
£ 900.
From it 'x' which satisfies the equation sin x = cos2x
Solution :
We plot the graph by taking the values of x and y.
Click here to enlarge
Fig. 29
The solution of y = sin x and y = cos 2x is given by the point of intersection of the two
graphs at P and Q i.e. x = 45 0
and x = 225 0.
EXAMPLE 8
Solve graphically the equation cos x = sin (x +
30 0) for 0 0 £ x £ 90 0 (Take interval of
15 0)
Solution : We prepare the tables of values of x and y = cos x and y = sin (x +
30 0) as follows.
Click here to enlarge
Fig. 30
EXAMPLE 9 Plot the graphs of y = x and y = 3 sin x on the same coordinate system and
find the graph of their sum.
Solution :
EXAMPLE 10
Sketch the graph of f(x) = 10 sin x + 2 sin 2x. Find its period, maximum and minimum values.
Solution
The function f (x) = 10 sin x + 2 sin 2x has,
Fig. 32
Period (T) = 2p
Maximum value = 11 at x = 700 and
Minimum value = -11 at x = 2700
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