Question

Express the following as trigonometric ratios of some acute angles.
(i) sin 1185° (ii) tan 235°
(iii) sin (- 3333)
(iv) cot (-3888°) (v) tan 458°
(iv) cosec (-60°)
(vii) cos 500° (viii) sec 380°
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Answer 1

Answer:

Step-by-step explanation:

(i) sin 1185°   = Sin( 1080 + 105)° = Sin(3 * 360 + 105)°  = Sin105°

= Sin(90 + 15)°  = Cos 15°

ii) tan 235° = Tan (180 + 55)° = Tan 55°

(iii) sin (- 3333°) = - Sin(3333°)  = -Sin(3240 + 93)° = -Sin(360 *9 + 93)°

= - Sin93° = - Sin(90 + 3)° = - (Cos3°) = -Cos3°

(iv) cot (-3888°)  = - Cot(3888°) = -Cot(3600 + 288)° = -Cot 288° = -Cot(180 + 108)° = -Cot108° = -Cot(90 + 18°) = -(-Tan18°) = Tan18°

(v) tan 458°  = Tan (360 + 98)° = Tan 98°  = Tan (90 + 8)° = -Cot8°

(iv) cosec (-60°) = -Cosec60°

(vii) cos 500°  = Cos (360 + 140)° = Cos 140° = Cos(180 - 40)° = -Cos40°

(viii) sec 380° = Sec(360 + 20)° = Sec 20°

Answer 2

Step-by-step explanation:

(i) sin 1185 = Sin ( 1080 + 105 )

= Sin ( 3*360 + 105 )

= Sin 105

= Sin ( 90 + 15 ) = Cos 15

(ii) tan 235 = Tan ( 180 + 55 )

= Tan 55

(iii) sin ( -3333 ) = - Sin ( 3333 )

= -Sin ( 3240 + 93 )

= - Sin ( 360 *9 + 93 )

= Sin93 = - Sin (90 + 3) = - ( Cos3)

= - Cos3

(iv) cot ( -3888 ) = -Cot ( 3888 )

= - Cot ( 3600 + 288 ) = -Cot 288

= - Cot ( 180 + 180 ) = -Cot108

= -Cot ( 90 + 18 ) = - ( -Tan18 )

= Tan18

(v) Tan 458 = Tan ( 360 + 98 )

= Tan 98 = Tan ( 90 + 8 )

= -Cot8

(vi) Cosec ( -60 ) = - Cosec60

(vii) Cos 500 = Cos ( 360 + 140 )

= Cos 140 = Cos ( 180 - 40 )

= - Cos ( 180 - 40 )

= - Cos40

(viii) Sec 360 = Sec ( 360 + 20 )

= Sec 20

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