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

$\begin{gathered} \sec A=\frac{13}{12} \\ \sec A=\frac{1}{\cos } \\ \cos A=\frac{12}{13} \end{gathered}$

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

Let us find cotA

$\cot A=\frac{\cos A}{\sin A}=\frac{\frac{12}{13}}{-\frac{5}{13}}=-\frac{12}{5}=-2.4$

The value of cot A is -2.4