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SUPPLEMENTARY PROBLEMS
1. (a) Find the coordinates of each of the trigonometric point (i)
P(-2p ), (ii) P(4p ),
(iii) P(-3p /2), (iv)
P(-5p /2),
(v) P(-2p /3)
Ans. (i) (1,0), (ii) (1,0), (iii) (0,1), (iv) (0,-1) (v) (1/2,
- Ö3/2) (vi) (-1/2, - Ö3/2)
(b) (i) The trigonometric point P(t) has coordinates
( Ö3/2, 1/2) and 0 < t < p /2
find 't'. Ans. t
=p /6
(ii)  Find 't' Ans. t =
7p /4 (Note 3p /2 < t < 2p )
(iii)  p /2 < t < p Find 't' Ans. t =
2p / 3
2 (a) Find out whether the following functions are periodic and if so find their fundamental
period.
(i) f(x) = cos (5x + 7) (ii) f(x) = cos (3x - 4) (iii) f(x) = tan (2x +3)
(iv) f(x) = sin (8-3x)
Ans. (i) (2p/5) (ii) 2p/3 (iii) p/2 (iv)
2p/3
(b) Find a function with fundamental period.
(i) 3 (ii) p/2 (iii) p/3 (iv) 8 (v)
p2 (6) p + 2
Ans. (i) tan (px/3) (ii) sin 4x (iii) cos 6x (iv) sin
 (v) cos  (vi) tan 
3. Sketch the graphs of following for one wave length
(a) y = 3 sin 1/2x (b) y = 2 cosx = 2 sin
(p/2 + x)
Ans. graph(a) graph(b)
4. Construct the graph of each of the following :
a) y = sin 2x - cos 3x b) y = 3 sin x + 2 cos 3x
5. Find the amplitude, period, phase shift, maximum and minimum values of :
(a) y = 4 + 3 sin (3x - 2) (b) y = -3 + 3/4 sin (1/4x + 2)
(c) y = 4 cos
3px
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