Understanding Engineering Mathematics

6.3.4 Graphs of trigonometric functions

(i)

−p 0 2 p

2

− 2

2 sin ( 2 t + (^) )
p p p 5 p t
6 3
p
3
2 3 6
2 p
3
5 p
− 6
7 p
− 6 −
p
− 2
p
− 3
p
− 6
(ii)
0 t
3
− 3
3 cos ( 3 t − (^) ) = 3 sin (3t)
p p p 2 p
6 3 2 3
2 p
3
p
− 2
p
− 3
p
− − 6
p
2
6.3.5 Inverse trigonometric functions
A.
x sin−^1 x sin−^1 x cos−^1 x cos−^1 x
PV GS PV GS
(i) 0 0 nπ
π
2
2 nπ±
π
2
(ii)
1
2
π
6
nπ+(− 1 )n
π
6
π
3
2 nπ±
π
3
(iii) −
1
2
−
π
6
nπ+(− 1 )n+^1
π
6
2 π
3
2 nπ±
2 π
3