I am a beginner and I am reading the page Basic Algebra and Calculus of the Tutorial where there is the following example
theta = var('theta')
solve(cos(theta)==sin(theta), theta)
and there is no solution, but a human being and other systems, like Mathematica, are able to solve this simple equation. So I suppose there is a way to solve it with Sage. Can you show me how?
Using the keyword argument algorithm='sympy' leads to more success:
sage: solve(cos(theta)==sin(theta), theta, algorithm='sympy')
[ImageSet(Lambda(_n, 2*_n*pi + 5*pi/4), Integers),
ImageSet(Lambda(_n, 2*_n*pi + pi/4), Integers)]
Other possibilities :
sage: solve(((sin(theta)==cos(theta))/cos(theta)).trig_reduce(), theta)
[theta == 1/4*pi]
which is harder and incomplete,
sage: solve(sin(theta)==cos(theta), theta, to_poly_solve=True)
[theta == 1/4*pi + pi*z1971]
which is
more concise, and
already translated in Sage
but uses an undeclared and implicitly integer-valued variable.
HTH,
If you have Mathematica (or the Wolfram engine) installed, you can also try :
sage: mathematica.Solve(sin(theta)==cos(theta), theta)
{{theta -> ConditionalExpression[(-3*Pi)/4 + 2*Pi*C[1],
Element[C[1], Integers]]},
{theta -> ConditionalExpression[Pi/4 + 2*Pi*C[1], Element[C[1], Integers]]}}
Other Sage-usable solvers do not solve this explicitly.
Asked: 2023-08-04 22:34:13 +0200
Seen: 93 times
Last updated: Aug 05 '23
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