Question

Find the value of cot A given sec A =13/13 and csc A<0find answer as a decimal, not fractions

Answer 1

Hi

Is sec A = 13/12

Since secA = 13/12

`\begin{gathered} \sec A=(13)/(12) \\ \sec A=(1)/(\cos ) \\ \cos A=(12)/(13) \end{gathered}`

Since cscA < 0, that means angle A is in the 3rd or the 4th quadrant

Let us use the rule

`\sin ^2A+\cos ^2A=1`
`\sin ^2A+((12)/(13))^2=1`
`\begin{gathered} \sin ^2A=(25)/(169) \\ \sin A=-(5)/(13) \end{gathered}`

Let us find cotA

`\cot A=(\cos A)/(\sin A)=((12)/(13))/(-(5)/(13))=-(12)/(5)=-2.4`

The value of cot A is -2.4