Home

1cos2x

cos(2x), often written cos 2x, denotes the cosine of twice the angle x. It is a fundamental double-angle function in trigonometry and is frequently used in identities, solving equations, and integral calculus.

Key identities for cos(2x) arise from the double-angle formula cos(A+B) with A = B = x. The standard

- cos(2x) = cos^2 x − sin^2 x

- cos(2x) = 1 − 2 sin^2 x

- cos(2x) = 2 cos^2 x − 1

Domain and range: cos(2x) is defined for all real x, and its values lie in the interval

Periodicity and graph: cos(2x) has period π, reflecting the fact that the argument 2x doubles the frequency

Applications: cos(2x) appears in solving trigonometric equations, simplifying expressions via double-angle identities, and integrating functions involving

Note: If written as 1cos2x, this is an unusual shorthand; the conventional notation is cos(2x).

forms
are:
[−1,
1].
of
the
base
cosine
function.
The
graph
is
a
cosine
wave
with
the
same
amplitude
as
cos
x
but
compressed
horizontally
by
a
factor
of
2.
It
reaches
a
maximum
of
1
at
x
=
kπ
and
a
minimum
of
−1
at
x
=
π/2
+
kπ
for
integer
k.
cos(2x).
It
also
plays
a
role
in
Fourier
analysis
and
signal
processing,
where
it
represents
a
component
of
periodic
waveforms.