3 Routine clean-up

How do escan PowerExpand find its way intobe made to evaluate the ArcTan withform that takes two arguments?

Consider

c = Cos[phi];
s = Sin[phi];
ArcTan[c, s] // PowerExpand
ArcTan[s/c] // PowerExpand


which yieldyields

ArcTan[Cos[phi], Sin[phi]]
phi


Oddly, PowerExpandPowerExpand does not find its way with the two argument version of ArcTanArcTan. However, it does with the single argument ArcTanArcTan, as expected.

I like ArcTanto use ArcTan with two arguments since it does not suffer from division by zero unless numerator and denominator are zero.

How can I tell PowerExpand to find its way into all inverse triginometric functions How can I tell PowerExpand to find its way into all inverse triginometric functions (assuming positive real variables, etc)??

What side effect would I suffer, if I attach a rule What side effect would I suffer, if I attach a rule to (to PowerExpand?PowerExpand or better yet to inverse trigonometric functions?) to deal with to deal with ArcTan[c,s] as ArcTan[s/c]? What other identities around trigonometric and inverse trigonometric functions and the exponential function that would also fit such considerations?ArcTan[c, s] as ArcTan[s/c]? What other identities around trigonometric and inverse trigonometric functions and the exponential function that would also fit such considerations?

How do es PowerExpand find its way into the ArcTan with two arguments?

Consider

c = Cos[phi];
s = Sin[phi];
ArcTan[c, s] // PowerExpand
ArcTan[s/c] // PowerExpand


which yield

ArcTan[Cos[phi], Sin[phi]]
phi


Oddly, PowerExpand does not find its way with the two argument version of ArcTan. However, it does with the single argument ArcTan, as expected.

I like ArcTan with two arguments since it does not suffer from division by zero unless numerator and denominator are zero.

How can I tell PowerExpand to find its way into all inverse triginometric functions (assuming positive real variables, etc)?

What side effect would I suffer, if I attach a rule (to PowerExpand? or better to inverse trigonometric functions?) to deal with ArcTan[c,s] as ArcTan[s/c]? What other identities around trigonometric and inverse trigonometric functions and the exponential function that would also fit such considerations?

How can PowerExpand be made to evaluate the ArcTan form that takes two arguments?

Consider

c = Cos[phi];
s = Sin[phi];
ArcTan[c, s] // PowerExpand
ArcTan[s/c] // PowerExpand


which yields

ArcTan[Cos[phi], Sin[phi]]
phi


Oddly, PowerExpand does not find its way with the two argument version of ArcTan. However, it does with the single argument ArcTan, as expected.

I like to use ArcTan with two arguments since it does not suffer from division by zero unless numerator and denominator are zero.

How can I tell PowerExpand to find its way into all inverse triginometric functions (assuming positive real variables, etc)?

What side effect would I suffer, if I attach a rule to PowerExpand or better yet to inverse trigonometric functions to deal with ArcTan[c, s] as ArcTan[s/c]? What other identities around trigonometric and inverse trigonometric functions and the exponential function that would also fit such considerations?

2 edited tags; edited tags
1

How do es PowerExpand find its way into the ArcTan with two arguments?

Consider

c = Cos[phi];
s = Sin[phi];
ArcTan[c, s] // PowerExpand
ArcTan[s/c] // PowerExpand


which yield

ArcTan[Cos[phi], Sin[phi]]
phi


Oddly, PowerExpand does not find its way with the two argument version of ArcTan. However, it does with the single argument ArcTan, as expected.

I like ArcTan with two arguments since it does not suffer from division by zero unless numerator and denominator are zero.

How can I tell PowerExpand to find its way into all inverse triginometric functions (assuming positive real variables, etc)?

What side effect would I suffer, if I attach a rule (to PowerExpand? or better to inverse trigonometric functions?) to deal with ArcTan[c,s] as ArcTan[s/c]? What other identities around trigonometric and inverse trigonometric functions and the exponential function that would also fit such considerations?