Question

angle c is an acute angle with cos c = 5/9 and cot c = 5/√56. what are the values of sec c and tan c? sec c = 5/√56, tan c = √56/9 sec c = 9/5, tan c = √56/5 sec c = √56/9, tan c = 9/5 sec c = 9/5, tan c = √56/9

Explanation:

Step1: Recall the reciprocal identity for secant

The secant of an angle is the reciprocal of the cosine of the angle. Given $\cos C=\frac{5}{9}$, then $\sec C=\frac{1}{\cos C}$.
$\sec C=\frac{9}{5}$

Step2: Recall the reciprocal identity for tangent

The tangent of an angle is the reciprocal of the cotangent of the angle. Given $\cot C = \frac{5}{\sqrt{56}}$, then $\tan C=\frac{1}{\cot C}$.
$\tan C=\frac{\sqrt{56}}{5}$

Answer:

$\sec C=\frac{9}{5},\tan C=\frac{\sqrt{56}}{5}$