Angle (1A) Angles in Degree Angles in Radian Conversion between Degree and Radian Co-terminal Angles. Young Won Lim 7/7/14
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1 Ange (1A) Anges in Degee Anges in Radian Convesion between Degee and Radian Co-temina Anges
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3 Ange and Ac Length Cicumfeence Ac ength Ange Ac Length : Ac ength Ratio : 0 1 : Cicumfeence Tigonomety
4 Ac Length Ratio : Ac ength : Cicumfeence Ange in degee 0 d Ratio 0 1 Ange in adian Tigonomety
5 Degee and Radian Scaes : Ac ength : Cicumfeence Ange in degee 0 d Degee Scae Ratio Ange in adian 0 0 Radian Scae = 1.57 =.1 =.71 =.8 Tigonomety 5
6 Measuing Ange in Degee Cicumfeence Ac ength Ratio 0 1 0º d º Ange in degee 0 d 0 Cicumfeence 0º Ac ength : = 0 : d d = 0 Tigonomety
7 Measuing Ange in Radian Cicumfeence Ac ength Ratio 0 1 ad ad Ange in adian 0 Cicumfeence Ac ength : = : = Tigonomety 7
8 Unit Degee and Unit Radian Unit Degee Degee 1 degee d deg d = 0 = 180 deg deg If = (cicumfeence / 0 ) = 0 Unit Radian = 0 Radian 1 adian The unit degee is epesented fo the sake of expanation = ad = ad ad If = adius = = Tigonomety 8
9 Degee Radian Cicumfeenc e Degee d deg = 0 deg 0º Ac ength d deg 180 = 180 deg 180 d º Radian d 180 ad = ad Tigonomety 9
10 Radian Degee Cicumfeence ad Radian ad = ad Ac ength ad 180 = ad 180 ad Degee 180 deg = 0 deg Tigonomety 10
11 Degee Radian The Same Ange d deg d = deg 0 deg d ad = ad ad d degee = adian Degee d deg d 180 ad Radian Degee 180 deg ad Radian Tigonomety 11
12 We-known Anges in Degee Tigonomety 1
13 We-known Anges in Radian Tigonomety 1
14 We-known Anges (Degee Radian) degee adian 0 0 = 0 = / = / = / = / = / = / = / = / = / + / = / = / + / = / = / + / = 5/ = / + / = =.1 10 / + = 7/ =.5 5 / + = 5/ =.97 0 / + = / = / + = / = / + + / = 5/ = / + + / = 7/ = / + + / = 11/ = / + + / = =.8 Tigonomety 1
15 We-known Anges (Radian Degee) adian degee 0.0 x 180 / = x 180 / = x 180 / = x 180 / = x 180 / = x 180 / = x 180 / =.8 ad 1 ad / x 180 / = 90 x 180 / = 180 / x 180 / = 70 x 180 / = 0 ad ad 5 ad ad / x 180 / = 5 / x 180 / = 15 5/ x 180 / = 5 7/ x 180 / = 15 Tigonomety 15
16 Co-temina Ange (Mutipe Rotations) temina side initia side Co-temina Anges the same temina side the same initia side diffeent otations 1 = = 1 otation = otations singe otation singe otation f (θ 1 ) = f (θ ) = f (θ ) = f (θ) f {sin θ, cosθ, tan θ} Tigonomety 1
17 Mutipe Rotations Aow mutipe otations : Ac ength d : Distance taveed aong cicumfeence 0 d 0 1 = = 1 otation = otations d 1 = d = d = Tigonomety 17
18 Mutipe Rotations in Degee = 0 = 0 = 0 d 1 = d = d = 1 = d 1 0 = d 0 = d 0 = 0 = 1 0 = 0 1 = = 0 = 0 Tigonomety 18
19 Mutipe Rotations in Radian = = = d 1 = d = d = 1 = d 1 = d = d = = 1 = 1 = = = Tigonomety 19
20 Co-temina Ange (Revese Rotations) Co-temina Anges the same temina side initia side temina side the same initia side diffeent otations 1 = = 1 otation Negative Ange + Positive Ange - cockwise singe otation countecockwise f (θ 1 ) = f (θ ) = f (θ) f {sin θ, cos θ, tan θ} Tigonomety 0
21 Revese Rotations Conside the diection of otations + d 0 : Ac ength d : Dispacement (diected distance) o 0 d 0 d 0 - d 0 1 = = 1 otation d 1 = d = Tigonomety 1
22 Revese Rotations in Degee = 0 = 0 d 1 = d = 1 = d 1 0 = d 0 = 0 = = = 0 Tigonomety
23 Revese Rotations in Radian = = d 1 = d = 1 = d 1 = d = = 1 1 = = Tigonomety
24 Anges in the Standad Position temina side initia side Anges in the standad position Vetex is in the oigin of a ectangua coodinate system Initia side ies aong the positive x-axis + Positive Ange p 0 counte-cockwise p n p n = 0 n - Negative Ange n 0 cockwise p = n 0 p 0 n = p 0 n 0 Tigonomety
25 Positive and Negative Anges Positive Ange Negative Ange Tigonomety 5
26 Ac Length Ratio f d i = d i f 1.0 d 1.0 d i d i g d i = Remainde d i g d j 1.0 d d j ± k 0 d j d j Tigonomety
27 Co-temina Ange & Ac Length Ratio g d i = Remainde d i Degee Degee 0 d i g d i 0 g d i d g d i = Remainde d i Radian Radian d i g d i g d i d Tigonomety 7
28 Refeences [1] [] [] Bitze, R. Ageba & Tigonomety. d ed, Pentice Ha [] Smith, R. T., Minton, R. B. Cacuus: Concepts & Connections, Mc Gaw Hi [5] 홍성대, 기본 / 실력수학의정석, 성지출판
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