How do you solve cot x = 2.3?

1 Answer
Trevor Ryan.
Oct 13, 2015

x={23,5^@+kpi}uu{203,5^@+kpi} ; k in ZZ

Explanation:

Since cotx=1/(tanx), we may write this equation as

1/(tanx)=2,3

therefore tanx=1/(2,3)

therefore x=tan^(-1)(1/(2,3))=23,5^@

But since tan is positive in both the first and 3rd quadrants, it can also be that x=180^@+23,5^@=203,5^@

Now since the tan graph is repetitive with period of pi, it implies that any integer multiples of pi added to these values will also provide a solution tot he original equation, that is,
x={23,5^@+kpi}uu{203,5^@+kpi} ; k in ZZ

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