Projects - Cengage Learning

C-50 Appendix C
MINI PROJECT
Identities and Graphs
An identity is an assertion that two functions are equal for every value in their
common domain. In this mini project you will use your graphing utility to
visualize identities.
Exercise
0 0
Graph each pair of equations. If a pair of graphs suggests an identity, then state
the identity clearly with a carefully stated domain. If a pair does not suggest an
identity then exhibit a counterexample, that is, a value of the domain variable
at which the function values are not the same. For trigonometric functions
the variables represent angles in radians. So, in parts (e) through (j), make
sure you are working in radian mode and try starting with a window of
[2p, 2p, p6] by [1, 1, 0.25] and then vary the size.
(a) y x 2 2x 1 and y (x 1) 2
t 2 9
(b) y
t 3
and y t 3
(c) y 2x 2 9 and y x 3
p 1 1, if p 1
(d) y and y b
p 1
1, if p 1
(e) y cos 2 u sin 2 u and y 1
(f) y sec 2 a 1 and y tan 2 a
(g) y sin 2u and y 2 sin u
(h) y cos 2b and y cos 2 b sin 2 b
(i) y cos(a ( p3)) and y cos a cos ( p3)
(j) y cos 3u 13 sin 3u and y 2 cos(3u ( p3))