WOLFRAM|DEMONSTRATIONS PROJECT

Series Expansions of Powers of Trigonometric Functions

​
function
Sin
order
power
clip bounding region
sin(x) ≈ x-
3
x
6
+
5
x
120
-
7
x
5040
+
9
x
362880
-
11
x
39916800
+
13
x
6227020800
-
15
x
1307674368000
+
17
x
355687428096000
-
19
x
121645100408832000
+
21
x
51090942171709440000
-
23
x
25852016738884976640000
+
25
x
15511210043330985984000000
-
27
x
10888869450418352160768000000
+
29
x
8841761993739701954543616000000
+O(
31
x
)
Taylor and Laurent series of powers of six trigonometric functions
sin
,
cos
,
tan
,
cot
,
sec
, and
csc
at the origin.