Given csc A = radical 85 over 2 and that angle A is in Quadrant I, find the exact value of sec A in simplest radical form using a rational denominator.

Answer 1

csc A = radical 85/2

sin A = inverse of csc A = 2/radical 85

sin(A)**2 + cos(A)**2 = 1

4

---- + cos(A)**2 = 1

85

cos(A)**2 = 1 - 4/85 = 81/85

cos(A) = +/- 9/radical 85

since we are in quadrant 1, cos(A) is positive and equals 9/radical 85

sec A is the inverse of cos A and is equal to radical 85/9 = 1.02