Find the values of the following trignometric ratios:
(a) `"cos"480^(@)`
(b) `sin 1125^(@)`
( c)` tan(-480^(@))`
( d) `"cosec"(-1200^(@))`

Explanation

( a) `cos480^(@)= cos(90^(@) xx 5 + 30^(@))`
Since `480^(@)` lies in the II quadrant in which the cosine function is negative and the multiple of `90^(@)` is also odd.
`therefore cos 480^(@)=-sin 30^(@)=-1/2`
(b) `sin 1125^(@)= sin(90^(@) xx 12+45^(@))`
Clearly, `1125^(@)` lies in the I quadrant and the multiple of `90^(@)` is even.
`therefore sin1125^(@)=sin45^(@)=1/sqrt(2)`
( c) `tan(-480^(@))=-tan480^(@)=-tan (90^(@) xx 5+30^(@))`
Since, `480^(@)` lies in the II quadrant and the multiple of `90^(@)` is odd.
`therefore -tan 480^(@)=-(-cot 30^(@)) = sqrt(3)`
( d) `"cosec"(-1200^(@))=-"cosec"1200^(@)=-"cosec"(90^(@) xx 13+30^(@))`
Since, `1200^(@)` lies in the II quadrant and the multiple of `90^(@)` is odd.
`therefore cos(-1200^(@))=-(sec 30^(@))=-2/sqrt(3)`.