How do you solve $cot x= -0.6$ between $(3pi)/2 ≤ x ≤ 2pi$ ?

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Answer 1 · 2015-04-22T19:27:28

The value of $x$ for $cot(x) = 0.6$
does not appear to be a standard or easily derivable value.

If you have access to the acot() function (in a table, on a calculator, or through some computer program) you could look it up directly.

What I did was
$tan(x) = 1/cos(x) = 1/(-0.6) = -1.666[6..]$

$x=arctan(tan(x)) = arctan(1.666[6..])$

I fortunately had access to the Excel spreadsheet function to evaluate this as =ATAN(-1.66667)

which gave a negative angle value
that could then be converted into the desired range by adding $2pi$

Final (approximate) result
$x = 5.2528$

How do you solve cot x= -0.6cot x= -0.6 between (3pi)/2 ≤ x ≤ 2pi(3pi)/2 ≤ x ≤ 2pi?