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in Trigonometry by (51.9k points)

Find the values of the following trigonometric ratios:

(i) sin 5π/3

(ii) sin 17π

(iii) tan 11π/6

(iv) cos (-25π/4)

(v) tan 7π/4

(vi) sin 17π/6

(vii) cos 19π/6

1 Answer

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(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

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