Why do I get the wrong answer for inverse sine 0.5 in degrees mode?

Exactly what were you trying to do? It helps to understand the problem you are having. Usually it means that the result exceeds the capacity of the memory (Too big). The upper limit for the calculator is 9.9999999.. *10^(99) or 10^100.

how can i calculate inverse of a matrix by casio fx 4500PA

The sine and cosine function have a range between [-1, 1]. The domain of their inverse functions is [-1,1]. So 20/1 which is 20 is out of the domain of definition of the functions. No limitations for tangent and cotangent.

The sine of 0.5 radians is about 0.4794, so your calculator seems to be giving you the correct answer in that case.

The sine of 0.5 degrees is about 0.00872, which your calculator may be displaying as something line 8.72 times ten to the negative 3. Look to the far right end of the number: do you see "x10-3" with the "-3" superscripted? In that case, again your calculator is giving you the correct answer.

On the fx-260, press 5 / 9 = SHIFT SIN .

On the fx-300MS, press SHIFT SIN ( 5 / 9 ) = .

Your question (?) is not clear so I will not try to guess what you really mean.
Be it as it may, the Casio FX-9860G SD can solve a polynomial equation of degree 2 or 3 with REAL coefficients. If the complex MODE is set to REAL it will find the real roots. If the complex mode is set to a+ib, it will find the real and complex roots.

Apparently it will take coefficients that are real, and will give a Ma Error if any coefficient is complex.

The inverse sine is defined only for numbers in the range [-1, +1].
The sine of a number is at most 1.0. There is no number whose sine is 1.5, which is what you're asking for.
The same applies to the cosine and inverse cosine.

You must configure the default angle unit to be degree.
In Run screen press the [SHIFT][MENU] to access the (SetUp) screen. Use the down arrow to scroll till you highlight the line Angle. The bottom of screen will then display three tabs at the bottom. Press the [F1] key to select [Degree].

Hello,
It may be due to the angle unit used. You can have angles in degrees, in radians, and in grads. You should set the default angle unit to waht you problem calls for.
To set degree as default SHIFT MODE 3
To set radians as default SHIFT MODE 4
To set grads as default SHIFT MODE 5

The values of angles calculated by the inverse trigonometric functions are in the default unit that is set . This may be the source of the wrong answers that you get.

Hope it helps.

Hello,
It may be due to the angle unit used. You can have angles in degrees, in radians, and in grads. You should set the default angle unit to waht you problem calls for.
To set degree as default SHIFT MODE 3
To set radians as default SHIFT MODE 4
To set grads as default SHIFT MODE 5

The values of angles calculated by the inverse trigonometric functions are in the default unit that is set . This may be the source of the wrong answers that you get.

Hope it helps.