Question

Given tan A = 7/5 and that angle A is in quadrant 1, find the exact value of csc A in simplest form using a rational denominator

Answer 1

`Tan A = (7)/(5) \\`

Consider right angle triangle ABC,∠B= 90°.

`tan = (Opposite)/(Adjacent) \\\\We \ get \ opposite = 7 \ and \ adjacent = 5\\hypotenuse^(2)= opposite^(2)+adjacent^(2)\\\\`

`= 49+25 = 74\\hypotenuse^(2) = 74\\hypotenuse = √(74) \\\\Sin A = (Opposite)/(hypotenuse) = (7)/(√(74) )`

`cosec A = (1)/(sinA) = (1)/((7)/(√(74) ) ) = (√(74) )/(7)`