Question

How do you solve `cot x = 2.3`?

Answer 1

`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`