puzzled by <a b/c> key in home vs cas for sin(45) degrees

[Liamtoh Resu]

I am puzzled by:

In home mode , evaluating SIN(45) gives three answers when cycling it
with the <a b/c> key: the irrational fraction, a decimal approximation,
and a fractional approximation.

In cas mode, evaluating sin(45) gives the irrational fraction at first.
Cycling the <a /bc> key alternates between the decimal approximation
and the fractional approximation.

I would have thought in cas mode then <a b/c> key would also show
the irrational fraction as well.

Any feed back would be appreciated.

Thanks.

[Joe Horn]

(07-14-2021 01:08 AM)Liamtoh Resu Wrote:  I am puzzled by:

In home mode , evaluating SIN(45) gives three answers when cycling it
with the <a b/c> key: the irrational fraction, a decimal approximation,
and a fractional approximation.

In cas mode, evaluating sin(45) gives the irrational fraction at first.
Cycling the <a /bc> key alternates between the decimal approximation
and the fractional approximation.

I would have thought in cas mode then <a b/c> key would also show
the irrational fraction as well.

Any feed back would be appreciated.

Thanks.

As you noticed, the [a b/c] key behaves very differently in Home and in CAS modes. This is intentional. In Home mode, that key only toggles between multiple representations of the most recent result (or the selected result) as a display fiction, without actually changing the result or generating a new result. In CAS mode, however, that key either performs the approx() function or the exact() function on the most recent result, thereby generating an entirely new result.

Press [Help] [Keys] [a b/c] to see the built-in explanation of the above distinction.

"If Home and CAS behaved the same way, there would be no need to have both of them. They are different tools for different tasks." -- Joe Horn

[Albert Chan]

FYI, the irrational fraction is a guess, from decimal float.

(SIN(45) - 35E-12) to (SIN(45) + 34E-12) all guessed irrational fraction √(1/2)