(i) Given as

sin (-11π/6)

sin (-11π/6) = sin (-330^°)

= – sin (90 × 3 + 60)^°

Here, 330^° lies in the IV quadrant in which the sine function is negative.

sin (-330^°) = – sin (90 × 3 + 60)^°

= – (-cos 60^°)

= – (-1/2)

Thus, 1/2

(ii) Given as

cosec (-20π/3)

cosec (-20π/3) = cosec (-1200)^°

= – cosec (1200)^°

= – cosec (90 × 13 + 30)^°

Here, 1200^° lies in the II quadrant in which cosec function is positive.

cosec (-1200)^° = – cosec (90 × 13 + 30)^°

= – sec 30^°

= -2/√3

(iii) Given as

tan (-13π/4)

tan (-13π/4) = tan (-585)^°

= – tan (90 × 6 + 45)^°

Here, 585^° lies in the III quadrant in which the tangent function is positive.

tan (-585)^° = – tan (90 × 6 + 45)^°

= – tan 45^°

= -1

(iv) Given as

cos 19π/4

cos 19π/4 = cos 855^°

= cos (90 × 9 + 45)^°

Here, 855^° lies in the II quadrant in which the cosine function is negative.

cos 855^° = cos (90 × 9 + 45)^°

= – sin 45^°

= – 1/√2

(v) Given as

sin 41π/4

sin 41π/4 = sin 1845^°

= sin (90 × 20 + 45)^°

Here, 1845^° lies in the I quadrant in which the sine function is positive.

sin 1845^° = sin (90 × 20 + 45)^°

= sin 45^°

= 1/√2

(vi) Given as

cos 39π/4

cos 39π/4 = cos 1755^°

= cos (90 × 19 + 45)^°

Here, 1755^° lies in the IV quadrant in which the cosine function is positive.

cos 1755^° = cos (90 × 19 + 45)^°

= sin 45^°

= 1/√2

(vii) Given as

sin 151π/6

sin 151π/6 = sin 4530^°

= sin (90 × 50 + 30)^°

Here, 4530^° lies in the III quadrant in which the sine function is negative.

sin 4530^° = sin (90 × 50 + 30)^°

= – sin 30^°

Thus, -1/2