(a) Use the Constant Difference Theorem (4.8.3) to show that if f ′ x = g ′ x for all x in the interval − ∞ , + ∞ , and if f and g have the same value at some point x 0 , then f x = g x for all x in − ∞ , + ∞ . (b) Use the result in part (a) to confirm the trigonometric identity sin 2 x + cos 2 x = 1 .
(a) Use the Constant Difference Theorem (4.8.3) to show that if f ′ x = g ′ x for all x in the interval − ∞ , + ∞ , and if f and g have the same value at some point x 0 , then f x = g x for all x in − ∞ , + ∞ . (b) Use the result in part (a) to confirm the trigonometric identity sin 2 x + cos 2 x = 1 .
(a) Use the Constant Difference Theorem (4.8.3) to show that if
f
′
x
=
g
′
x
for all
x
in the interval
−
∞
,
+
∞
,
and if
f
and
g
have the same value at some point
x
0
,
then
f
x
=
g
x
for all
x
in
−
∞
,
+
∞
.
(b) Use the result in part (a) to confirm the trigonometric identity
sin
2
x
+
cos
2
x
=
1
.
Equations that give the relation between different trigonometric functions and are true for any value of the variable for the domain. There are six trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant.
Find the smallest interval in x over which the functions sin(x/xo) and
cos(Tx/xo) are orthogonal. On the same interval, are the following pairs
of functions orthogonal?
a) sin(x/x₁) and sin(2πx/xo).
b) sin(x/xo) and sin(x/xo).
c) sin(x/xo) and sin(x/2x).
Show that the graphs of cos(x) and
tersect at a point whose x-coordinate c = [0; 2π].
X
in-
#7 4.8
Chapter 4 Solutions
Calculus Early Transcendentals, Binder Ready Version
University Calculus: Early Transcendentals (4th Edition)
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