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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