Find the values of the following trignometric ratios:
(a) `tan (19pi)/3`

Explanation

(a) `(19pi)/3= (19/3 xx 180^(@)) = 1140^(@) = 90^(@) xx 12+60^(@)`
Clearly, it lies in the 1st quadrant and the multipleof `90^(@)` is even.
`therefore tan(19pi)/3=tan(90^(@) xx 12+60^(@))`
`=tan60^(@) =sqrt(3)`
(b) `(11pi)/3 = ((11 xx 180)/(3))^(@)=660^(@)=90^(@) xx 7 + 30^(@)`
Clearly, it lies in the IVth quadrant and the multiple of `90^(@)` is odd.
`sin(-11pi)/(3) = -sin(11pi)/3 = -sin(90^(@) xx 7+30^(@))=-(-cos 30^(@))`
`=-(-sqrt(3)/2)=sqrt(3)/2`.