Question

Find the exact value.

Answer 1

`\text{Given that,}\\\\\cot A = -(9)/(√(40))\\\\\\\implies \tan A = -\frac{√(40)}9\\\\\\\implies \tan^2 A = (40)/(81)\\\\\\\implies \sec^2 A -1 = (40)/(81)\\\\\implies \sec^2 A = 1 + (40)/(81)\\\\\implies \sec^2 A = (121)/(81)\\\\\implies \sec A = \pm \sqrt{(121)/(81)}= \pm(11)/(9)\\\\\\\text{Since the angle A is in quadrant II, the value of sec A will be negative.}\\\\\\\text{Hence,}~ \sec A=-(11)/(9)`