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
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# 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?