sin(x)^2

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Eth
Eth 2019-4-8
How to expand a function like sin(x)^2 to output 1/2*(1-cos(2*x))? I tried expand(sin(x)^2) but it returns the same.

采纳的回答

Star Strider
Star Strider 2019-4-8
Use the rewrite function:
syms x
ys = sin(x)^2;
ye = rewrite(ys, 'exp')
yc = rewrite(expand(ye), 'cos')
p[roducing:
yc =
1/2 - cos(2*x)/2
  2 个评论
Eth
Eth 2019-4-8
Thanks.
Star Strider
Star Strider 2019-4-8
As always, my pleasure.

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更多回答(2 个)

Hose Orlando
Hose Orlando 2020-8-3
how do i put this matrix into matlab

Carlos Guerrero García
Perhaps the following lines will be useful:
syms x; % Establishing 'x' as a symbolic variable
combine(sin(x)^2,'sincos') % For the 1st (original) question
ans = 
combine(sin(x)^3,'sincos') % For the last question
ans = 
  1 个评论
John D'Errico
John D'Errico 2022-11-22
Note that combine is a useful tool, but one we see mentioned here rarely. So...
help sym/combine
combine Combine terms of the same algebraic structure. combine(S) tries to rewrite products of powers in the expression S as a single power. combine(S, T) combines several calls to the target function T in the expression f to a single call. The target T is specified as one of the strings 'atan', 'exp', 'gamma', 'log', 'sincos', 'sinhcosh'. combine(..., 'IgnoreAnalyticConstraints',VAL) controls the level of mathematical rigor to use on the analytical constraints while combining (branch cuts, division by zero, and so on). Here, VAL can be TRUE or FALSE. If you use TRUE, then combine uses a set of mathematical rules, such as ln(a) + ln(b) = ln(a*b), that are not generally correct, but can give simpler results. The default is FALSE. Examples: combine(2^x * 3^x) returns 6^x combine((2^x)^i) returns (2^x)^i combine((2^x)^i, 'IgnoreAnalyticConstraints', true) returns 2^(x*i) combine(log(x) + log(y), 'log') returns log(x) + log(y) combine(log(x) + log(y), 'log', 'IgnoreAnalyticConstraints', true) returns log(x*y) See also sym/simplify, sym/expand, sym/factor Documentation for sym/combine doc sym/combine

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