182 Alphabetical Listing
tCollect()
Catalog >
tCollect(Expr1) ⇒ expression
Returns an expression in which products
and integer powers of sines and cosines are
converted to a linear combination of sines
and cosines of multiple angles, angle sums,
and angle differences. The transformation
converts trigonometric polynomials into a
linear combination of their harmonics.
Sometimes tCollect() will accomplish your
goals when the default trigonometric
simplification does not. tCollect() tends to
reverse transformations done by tExpand().
Sometimes applying tExpand() to a result
from tCollect(), or vice versa, in two
separate steps simplifies an expression.
tExpand()
Catalog >
tExpand(Expr1) ⇒ expression
Returns an expression in which sines and
cosines of integer-multiple angles, angle
sums, and angle differences are expanded.
Because of the identity (sin(x))2+(cos
(x))2=1, there are many possible equivalent
results. Consequently, a result might differ
from a result shown in other publications.
Sometimes tExpand() will accomplish your
goals when the default trigonometric
simplification does not. tExpand() tends to
reverse transformations done by tCollect().
Sometimes applying tCollect() to a result
from tExpand(), or vice versa, in two
separate steps simplifies an expression.
Note: Degree-mode scaling by π/180
interferes with the ability of tExpand() to
recognize expandable forms. For best
results, tExpand() should be used in Radian
mode.
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