Given tan A=5/6 and that angle A is in Quadrant I, find the exact value of csc A in simplest radical form using a rational denominator.

Answer 1

Since tan(A) = 5/6

And equation of tangent = sine/cosine which we use to find the csc(A)

Set

tan(A)= (5)/(6)= (sin(A))/(cos(A))

we know tan (pi/4) = tan (45 degrees) = 1 (So the A should be around value 1 which is in radians)

given tan (A) = (sin(A))/(cos(A)) = (5)/(6) so sin(A) = 5

just plug in sin(A)=5 into cosecant equation : csc(angle in radians)=1/(sin(angle in radians)) :

1/(5)= 1/5 = csc(A)

is the answer!!