(i) Given as
sin 5π/3
5π/3 = (5π/3 × 180)°
= 300°
= (90 × 3 + 30)°
Here, 300° lies in IV quadrant in which sine function is negative.
sin 5π/3 = sin (300)°
= sin (90 × 3 + 30)°
= – cos 30°
Thus, – √3/2
(ii) Given as
sin 17π
Sin 17π = sin 3060°
= sin (90 × 34 + 0)°
Since, 3060° lies in the negative direction of x-axis i.e., on boundary line of II and III quadrants.
Sin 17π = sin (90 × 34 + 0)°
= – sin 0°
= 0
(iii) Given as
tan 11π/6
tan 11π/6 = (11/6 × 180)°
= 330°
Since, 330° lies in the IV quadrant in which tangent function is negative.
tan 11π/6 = tan (300)°
= tan (90 × 3 + 60)°
= – cot 60°
= – 1/√3
(iv) Given as
cos (-25π/4)
cos (-25π/4) = cos (-1125)°
= cos (1125)°
Since, 1125° lies in the I quadrant in which cosine function is positive.
cos (1125)° = cos (90 × 12 + 45)°
= cos 45°
= 1/√2
(v) Given as
tan 7π/4
tan 7π/4 = tan 315°
= tan (90 × 3 + 45)°
Since, 315° lies in the IV quadrant in which tangent function is negative.
tan 315° = tan (90 × 3 + 45)°
= – cot 45°
= -1
(vi) Given as
sin 17π/6
sin 17π/6 = sin 510°
= sin (90 × 5 + 60)°
Since, 510° lies in the II quadrant in which sine function is positive.
sin 510° = sin (90 × 5 + 60)°
= cos 60°
= 1/2
(vii) Given as
cos 19π/6
cos 19π/6 = cos 570°
= cos (90 × 6 + 30)°
Here, 570° lies in III quadrant in which cosine function is negative.
cos 570° = cos (90×6 + 30)°
= – cos 30°
Thus, – √3/2