Question #07ebb

1 Answer
Aug 13, 2016

Answer:

Invalid as a general formula..

Explanation:

The principal value from the calculator for #arctan(y/x) in Q1#

when #(x, y) in Q1 or Q3 #.

Likewise,

the principal value from the calculator for

#arc tan (y/x) in Q2#, when #(x, y) in Q2 or Q4#

Test with #(x, y)=(+-1, +-1)#

Any formula equivalent to the couple

# 'cos theta = x/r and sin theta = y/r'#, for fixing #theta#, is valid.

As sine and cosine are periodic with period #2pi#, #theta# identified

in #[0, 2pi]# would fix the quadrant correctly.
.