Question

given cot A= 40/9 and that angle A is in quadrant 1 find the exact value of sec A in the simplest radical form using a rational denominator

Answer 1

41/40

Explanation:

Given cotA = 40/9

1/tanA = 40/9

tanA = 9/40

According to SOH, CAH, TOA

tan A = 9/40 = opposite/adjacent

Get the hypotenuse

hyp² = opp²+adj²

hyp² = 9²+40²

hyp² = 81+1600

hyp² = 1681

hyp = √1681

hyp = 41

Het sec A

sec A = 1/cosA

Since cos A = adjacent/hypotenuse

cos A = 40/41

secA = 1/(40/41)

SecA = 41/40

Hence the exact value of secA is 41/40