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arcsin(5/24*cos(45)) is a Sage object representing the quantity you want to manipulate. What you are seeking is a numerical approximation of this quantity. Which can be obtained by :

sage: numerical_approx(arcsin(5/24*cos(45)))
0.109661742042478

or

sage: arcsin(5/24*cos(45)).n()
0.109661742042478

Try numerical_approx?...

arcsin(5/24*cos(45)) is a Sage object representing the quantity you want to manipulate. manipulate; its value is a real number+. What you are seeking is a numerical approximation of this quantity. quantity expressed as a decimal representation. Which can be obtained by :

sage: numerical_approx(arcsin(5/24*cos(45)))
0.109661742042478

or

sage: arcsin(5/24*cos(45)).n()
0.109661742042478

Try numerical_approx?...

I want to have the expression as a real number

arcsin(5/24*cos(45)) is a Sage object representing the quantity you want to manipulate; its value is a real number+. What you are seeking is a numerical approximation of this quantity expressed as a decimal representation. Which can be obtained by :

sage: numerical_approx(arcsin(5/24*cos(45)))
0.109661742042478

or

sage: arcsin(5/24*cos(45)).n()
0.109661742042478

Try numerical_approx?...

• Note that there are an infinity of complex values whose $\sin$ is 5/24*cos(45) ; the mathematical function $\arcsin$ is multivalued. The Sage function arcsin implement aparticular choice of this branch cut, returning a value in the interval $[-\frac\pi2\ \frac\pi2}$.\frac\pi2]$.

I want to have the expression as a real number

arcsin(5/24*cos(45)) is a Sage object representing the quantity you want to manipulate; its value is a real number+. What you are seeking is a numerical approximation of this quantity expressed as a decimal representation. Which can be obtained by :

sage: numerical_approx(arcsin(5/24*cos(45)))
0.109661742042478

or

sage: arcsin(5/24*cos(45)).n()
0.109661742042478

Try numerical_approx?...

• Note that there are an infinity of complex values whose $\sin$ is 5/24*cos(45) ; the mathematical function $\arcsin$ is multivalued. The Sage function arcsin implement aparticular choice of this branch cut, returning a value in the interval $[-\frac\pi2\ \frac\pi2]$.