(a) 30 o = 25.8 o. [ rad] (b) 45 o = (c) 81.5 o = [ rad] (e) 154 o 20 = [2.144 rad] (g) -50 o = [3.938 rad]

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1 CIRCULR MESURE. RDIN. Conveting Measuements in Radians to Degees and Vice Vesa S Definition: ad whee S is the length of the ac, is the adius of the cicle, and θ is the angle subtended at the cente by the ac. Fo the full cicle, the cicumfeence is π and the angle is 60 o. Theefoe,. ad Hence, π ad = 60 o => π ad = 80 o S Fo each of the following measuement in degee, change it to adian. 5.8 o (a) 0 o = Since 80 o = π ad π ad 5.8 o [0.57 ad] (b) 45 o = (c) 8.5 o = (d).8 o = [ ad] (e) 54 o 0 = [.4 ad] (f) 5 o 6 = [.44 ad] (g) -50 o = [.694 ad] [.98 ad] Cicula Measue [ ad]

2 Fo each of the following measuement in adian, change it to degee ad (a) 0.6 ad = Since π ad = 80 o ad 0.75 π 0.75 ad 4.97 lways use π =.4 (b).54 ad = (c) 8 ad 5 [4.7 o ] (d) ad 7 [88. o ] (e).π ad = [06.4 o ] (f) π ad [9. o ] (g) -0.5 ad = [6 o ] (h) - ad [60 o ] (i) ( + π) ad = [-4. o ] [-.67 o ] [7.9 o ] Cicula Measue

3 . RC LENGTH F CIRCLE. c Length, Radius and ngle S => S = θ Fo each of the following, find the length of the ac S given the values of and θ. (a) = 0 cm and θ = 0.6 ad = and θ =.5 ad Since S = θ = 0.5 = 5 cm S.5 ad (b) = 5 cm and θ =.4 ad (c) = 0 cm and θ = 6 ad [ cm] (d) = and θ = 60 o [ cm] (e) =.5 m and θ = 8.8 o [5.7 cm] [0.47 cm] [.68 m] Fo each of the following, calculate the length of the adius given the values of S and θ. (a) S = 9 cm and θ =.5 ad S = 4.5 cm and θ =.5 ad Since S = θ 4.5 =.5.5 ad = cm (b) S = 4.5 cm and θ =.8 ad 4.5 cm (c) S = 9 m and θ = 0 o [6 cm] (d) S = 5 cm and θ =.8 o [.5 cm] (e) S = and θ = 8 ad [7.9 m] [6.0 cm] Cicula Measue [5.46 cm]

4 Fo each of the following, find the angle θ in adian given the values of and S. (a) = 9 cm and S = 6 cm = 5 cm and S = Since S = θ 0 = 5θ 0 θ = 5 = ad (b) = 7 cm and S = 5.6 cm 5 cm (c) = 0 cm and S = 0.7 m [4 ad] (d) =. cm and S = 0 cm [0.8 ad] (e) =.5 cm and S = cm [.5 ad] [6 cm] [ cm] Fo each of the following, find the angle θ in degee given the values of and S. (a) = and S = 6 cm = 8 cm and S = 0 cm Since S = θ 0 = 8θ 0 θ = ad 8 8 cm 0 cm =.5 80 = 4. o (b) = 5 cm and S = 5.4 cm (c) = 5.6 cm and S = cm [4.7 o ] (d) = 7.5 cm and S = 0.8 m [57.9 o ] (e) = 5.6 cm and S = π cm [.76 o ] [4.4 o ] Cicula Measue 4 [96.4 o ]

5 . RE F SECTR. ea of Secto, Radius and ngle ea of a cicle, = π ea fo a secto of angle θ o, 60 ad Conveting to adian, ad = θ, θ must be in adian. Fo each of the following, find the aea of the secto given the values of and θ. (a) = 5 cm and θ = 0.8 ad = cm and θ =.8 ad Since.8 = 8. cm.8 ad cm cm [ ] (b) =. cm and θ =.78 ad (c) =.7 cm and θ = ad 4 (d) = mm and θ = ad 5 [.96 cm ] (e) =.5 m and θ =.8 o [6.075 cm ] (f) = 5 m and θ = 85 o [80.98 mm ] (g) =. cm and θ = 67. o [.4 m ] [0.67 m ] [0.9 cm ] Cicula Measue 5

6 Fo each of the following, find the length of the adius given the values of θ and. θ =. ad and = 5 cm (a) θ = ad and = 6 cm Since ad = 5 = 5 cm [ cm] (b) θ =.4 ad and = 8. cm (c) θ = 6 ad and = π m (d) θ = 7 ad and = 78.5 cm [ cm] (e) θ = 0 o and = 5 cm [6 m] (f) θ = 65 o and = 78 cm [09.55 cm] (g) θ = 0 o and = 5 cm [5.54 cm] [.7 cm] [6.94 cm] Cicula Measue 6

7 Fo each of the following, find the angle θ in adian given the values of and. = 5 cm and = 9 cm (a) =.4 cm and =.44 cm 8 Since ad 4 (b) = 8 cm and = 64 cm 5 cm 5 cm 9 _ 8 cm (c) = 0.6 m and =.4 m [0.5 ad] [ ad] [8 ad] Fo each of the following, find the angle θ in degee given the values of and. = 4 cm and = 6 cm (a) = 5 cm and = 50π cm Since cm = ad 80 =.4 = 4.58 o 4 cm 4 cm (b) = 8 cm and = 48 cm (c) =. m and = 5 m [80 o ] [85.9 o ] [55.95 o ] Cicula Measue 7

8 . eimete of Segments of a Cicle Fo the shaded segment in the given diagam beside, find its peimete. The peimete of the shaded segment is the total length of the ac and the chod. S = θ = 0. = cm To find the length of the chod, conside the tiangle in the diagam beside. sin 0.6 ad 0 = 80 0 sin(0.6 ).4 = = =.9 cm peimete of shaded segment = +.9 =.9 cm 0.6 ad 0.6 ad. ad Note: The length of the chod = sin. ea of Segments of a Cicle With efeence to the secto in the same diagam beside, find the aea of the shaded segment. The aea of the shaded segment is the diffeence between the aea of the secto and the tiangle.. ad ea of secto = θ 0. = 60 cm To find the aea of the tiangle, please efe to the diagam beside. C is pependicula to the adius. C sin. ad 80 C sin..4 ea of C sin cm ea of shaded segment = =.40 cm. ad C ea of segment sin sin Note: ea of tiangle = sin Cicula Measue 8

9 Fo each of the following diagams, find (i) the peimete and (ii) the aea of the shaded segment. (a) 5 cm (b) 0.5 ad 6 cm 0.8 ad 6 cm 5 cm (c) [eimete = cm, ea = cm ].8 cm (d) [eimete = 9.47 cm, ea =.489 cm ] 4. cm 60 o 4. cm ad.8 cm [eimete = 0.9 cm, ea =.45 cm ] [eimete = cm, ea = 4.87 cm ] Cicula Measue 9

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