Tabel Sinus Plus3

sin cos tan sin cos tan sin cos tan sin cos tan 0 o 0.000 1.000 0.000 45 o 0.707 0.707 1.000 90 o 1.000 0.000 ##### 135 o 0.707 -0.707 -1.0001 o 0.017 1.000 0.017 46 o 0.719 0.695 1.036 91 o 1.000 -0.017 -57.29 136 o 0.695 -0.719 -0.9662 o 0.035 0.999 0.035 47 o 0.731 0.682 1.072 92 o 0.999 -0.035 -28.64 137 o 0.682 -0.731 -0.9333 o 0.052 0.999 0.052 48 o 0.743 0.669 1.111 93 o 0.999 -0.052 -19.08 138 o 0.669 -0.743 -0.9004 o 0.070 0.998 0.070 49 o 0.755 0.656 1.150 94 o 0.998 -0.070 -14.30 139 o 0.656 -0.755 -0.8695 o 0.087 0.996 0.087 50 o 0.766 0.643 1.192 95 o 0.996 -0.087 -11.43 140 o 0.643 -0.766 -0.8396 o 0.105 0.995 0.105 51 o 0.777 0.629 1.235 96 o 0.995 -0.105 -9.514 141 o 0.629 -0.777 -0.8107 o 0.122 0.993 0.123 52 o 0.788 0.616 1.280 97 o 0.993 -0.122 -8.144 142 o 0.616 -0.788 -0.7818 o 0.139 0.990 0.141 53 o 0.799 0.602 1.327 98 o 0.990 -0.139 -7.115 143 o 0.602 -0.799 -0.7549 o 0.156 0.988 0.158 54 o 0.809 0.588 1.376 99 o 0.988 -0.156 -6.314 144 o 0.588 -0.809 -0.727

10 o 0.174 0.985 0.176 55 o 0.819 0.574 1.428 100 o 0.985 -0.174 -5.671 145 o 0.574 -0.819 -0.70011 o 0.191 0.982 0.194 56 o 0.829 0.559 1.483 101 o 0.982 -0.191 -5.145 146 o 0.559 -0.829 -0.67512 o 0.208 0.978 0.213 57 o 0.839 0.545 1.540 102 o 0.978 -0.208 -4.705 147 o 0.545 -0.839 -0.64913 o 0.225 0.974 0.231 58 o 0.848 0.530 1.600 103 o 0.974 -0.225 -4.331 148 o 0.530 -0.848 -0.62514 o 0.242 0.970 0.249 59 o 0.857 0.515 1.664 104 o 0.970 -0.242 -4.011 149 o 0.515 -0.857 -0.60115 o 0.259 0.966 0.268 60 o 0.866 0.500 1.732 105 o 0.966 -0.259 -3.732 150 o 0.500 -0.866 -0.57716 o 0.276 0.961 0.287 61 o 0.875 0.485 1.804 106 o 0.961 -0.276 -3.487 151 o 0.485 -0.875 -0.55417 o 0.292 0.956 0.306 62 o 0.883 0.469 1.881 107 o 0.956 -0.292 -3.271 152 o 0.469 -0.883 -0.53218 o 0.309 0.951 0.325 63 o 0.891 0.454 1.963 108 o 0.951 -0.309 -3.078 153 o 0.454 -0.891 -0.51019 o 0.326 0.946 0.344 64 o 0.899 0.438 2.050 109 o 0.946 -0.326 -2.904 154 o 0.438 -0.899 -0.48820 o 0.342 0.940 0.364 65 o 0.906 0.423 2.145 110 o 0.940 -0.342 -2.747 155 o 0.423 -0.906 -0.46621 o 0.358 0.934 0.384 66 o 0.914 0.407 2.246 111 o 0.934 -0.358 -2.605 156 o 0.407 -0.914 -0.44522 o 0.375 0.927 0.404 67 o 0.921 0.391 2.356 112 o 0.927 -0.375 -2.475 157 o 0.391 -0.921 -0.42423 o 0.391 0.921 0.424 68 o 0.927 0.375 2.475 113 o 0.921 -0.391 -2.356 158 o 0.375 -0.927 -0.40424 o 0.407 0.914 0.445 69 o 0.934 0.358 2.605 114 o 0.914 -0.407 -2.246 159 o 0.358 -0.934 -0.38425 o 0.423 0.906 0.466 70 o 0.940 0.342 2.747 115 o 0.906 -0.423 -2.145 160 o 0.342 -0.940 -0.36426 o 0.438 0.899 0.488 71 o 0.946 0.326 2.904 116 o 0.899 -0.438 -2.050 161 o 0.326 -0.946 -0.34427 o 0.454 0.891 0.510 72 o 0.951 0.309 3.078 117 o 0.891 -0.454 -1.963 162 o 0.309 -0.951 -0.32528 o 0.469 0.883 0.532 73 o 0.956 0.292 3.271 118 o 0.883 -0.469 -1.881 163 o 0.292 -0.956 -0.30629 o 0.485 0.875 0.554 74 o 0.961 0.276 3.487 119 o 0.875 -0.485 -1.804 164 o 0.276 -0.961 -0.28730 o 0.500 0.866 0.577 75 o 0.966 0.259 3.732 120 o 0.866 -0.500 -1.732 165 o 0.259 -0.966 -0.26831 o 0.515 0.857 0.601 76 o 0.970 0.242 4.011 121 o 0.857 -0.515 -1.664 166 o 0.242 -0.970 -0.24932 o 0.530 0.848 0.625 77 o 0.974 0.225 4.331 122 o 0.848 -0.530 -1.600 167 o 0.225 -0.974 -0.23133 o 0.545 0.839 0.649 78 o 0.978 0.208 4.705 123 o 0.839 -0.545 -1.540 168 o 0.208 -0.978 -0.21334 o 0.559 0.829 0.675 79 o 0.982 0.191 5.145 124 o 0.829 -0.559 -1.483 169 o 0.191 -0.982 -0.19435 o 0.574 0.819 0.700 80 o 0.985 0.174 5.671 125 o 0.819 -0.574 -1.428 170 o 0.174 -0.985 -0.17636 o 0.588 0.809 0.727 81 o 0.988 0.156 6.314 126 o 0.809 -0.588 -1.376 171 o 0.156 -0.988 -0.15837 o 0.602 0.799 0.754 82 o 0.990 0.139 7.115 127 o 0.799 -0.602 -1.327 172 o 0.139 -0.990 -0.14138 o 0.616 0.788 0.781 83 o 0.993 0.122 8.144 128 o 0.788 -0.616 -1.280 173 o 0.122 -0.993 -0.12339 o 0.629 0.777 0.810 84 o 0.995 0.105 9.514 129 o 0.777 -0.629 -1.235 174 o 0.105 -0.995 -0.10540 o 0.643 0.766 0.839 85 o 0.996 0.087 11.430 130 o 0.766 -0.643 -1.192 175 o 0.087 -0.996 -0.08741 o 0.656 0.755 0.869 86 o 0.998 0.070 14.301 131 o 0.755 -0.656 -1.150 176 o 0.070 -0.998 -0.07042 o 0.669 0.743 0.900 87 o 0.999 0.052 19.081 132 o 0.743 -0.669 -1.111 177 o 0.052 -0.999 -0.05243 o 0.682 0.731 0.933 88 o 0.999 0.035 28.636 133 o 0.731 -0.682 -1.072 178 o 0.035 -0.999 -0.03544 o 0.695 0.719 0.966 89 o 1.000 0.017 57.290 134 o 0.719 -0.695 -1.036 179 o 0.017 -1.000 -0.01745 o 0.707 0.707 1.000 90 o 1.000 0.000 ##### 135 o 0.707 -0.707 -1.000 180 o 0.000 -1.000 0.000

TABEL SINUS, COSINUS, DAN TANGEN

MGMP Fisika SMA Negeri 9 Kota Tangerang Selatanhttp://mgmpfisikasma9.wordpress.comPage 1 of 2

sin cos tan sin cos tan sin cos tan sin cos tan 180 o 0.000 -1.000 0.000 225 o -0.707 -0.707 1.000 270 o -1.000 0.000 ##### 315 o -0.707 0.707 -1.000181 o -0.017 -1.000 0.017 226 o -0.719 -0.695 1.036 271 o -1.000 0.017 -57.29 316 o -0.695 0.719 -0.966182 o -0.035 -0.999 0.035 227 o -0.731 -0.682 1.072 272 o -0.999 0.035 -28.64 317 o -0.682 0.731 -0.933183 o -0.052 -0.999 0.052 228 o -0.743 -0.669 1.111 273 o -0.999 0.052 -19.08 318 o -0.669 0.743 -0.900184 o -0.070 -0.998 0.070 229 o -0.755 -0.656 1.150 274 o -0.998 0.070 -14.30 319 o -0.656 0.755 -0.869185 o -0.087 -0.996 0.087 230 o -0.766 -0.643 1.192 275 o -0.996 0.087 -11.43 320 o -0.643 0.766 -0.839186 o -0.105 -0.995 0.105 231 o -0.777 -0.629 1.235 276 o -0.995 0.105 -9.514 321 o -0.629 0.777 -0.810187 o -0.122 -0.993 0.123 232 o -0.788 -0.616 1.280 277 o -0.993 0.122 -8.144 322 o -0.616 0.788 -0.781188 o -0.139 -0.990 0.141 233 o -0.799 -0.602 1.327 278 o -0.990 0.139 -7.115 323 o -0.602 0.799 -0.754189 o -0.156 -0.988 0.158 234 o -0.809 -0.588 1.376 279 o -0.988 0.156 -6.314 324 o -0.588 0.809 -0.727190 o -0.174 -0.985 0.176 235 o -0.819 -0.574 1.428 280 o -0.985 0.174 -5.671 325 o -0.574 0.819 -0.700191 o -0.191 -0.982 0.194 236 o -0.829 -0.559 1.483 281 o -0.982 0.191 -5.145 326 o -0.559 0.829 -0.675192 o -0.208 -0.978 0.213 237 o -0.839 -0.545 1.540 282 o -0.978 0.208 -4.705 327 o -0.545 0.839 -0.649193 o -0.225 -0.974 0.231 238 o -0.848 -0.530 1.600 283 o -0.974 0.225 -4.331 328 o -0.530 0.848 -0.625194 o -0.242 -0.970 0.249 239 o -0.857 -0.515 1.664 284 o -0.970 0.242 -4.011 329 o -0.515 0.857 -0.601195 o -0.259 -0.966 0.268 240 o -0.866 -0.500 1.732 285 o -0.966 0.259 -3.732 330 o -0.500 0.866 -0.577196 o -0.276 -0.961 0.287 241 o -0.875 -0.485 1.804 286 o -0.961 0.276 -3.487 331 o -0.485 0.875 -0.554197 o -0.292 -0.956 0.306 242 o -0.883 -0.469 1.881 287 o -0.956 0.292 -3.271 332 o -0.469 0.883 -0.532198 o -0.309 -0.951 0.325 243 o -0.891 -0.454 1.963 288 o -0.951 0.309 -3.078 333 o -0.454 0.891 -0.510199 o -0.326 -0.946 0.344 244 o -0.899 -0.438 2.050 289 o -0.946 0.326 -2.904 334 o -0.438 0.899 -0.488200 o -0.342 -0.940 0.364 245 o -0.906 -0.423 2.145 290 o -0.940 0.342 -2.747 335 o -0.423 0.906 -0.466201 o -0.358 -0.934 0.384 246 o -0.914 -0.407 2.246 291 o -0.934 0.358 -2.605 336 o -0.407 0.914 -0.445202 o -0.375 -0.927 0.404 247 o -0.921 -0.391 2.356 292 o -0.927 0.375 -2.475 337 o -0.391 0.921 -0.424203 o -0.391 -0.921 0.424 248 o -0.927 -0.375 2.475 293 o -0.921 0.391 -2.356 338 o -0.375 0.927 -0.404204 o -0.407 -0.914 0.445 249 o -0.934 -0.358 2.605 294 o -0.914 0.407 -2.246 339 o -0.358 0.934 -0.384205 o -0.423 -0.906 0.466 250 o -0.940 -0.342 2.747 295 o -0.906 0.423 -2.145 340 o -0.342 0.940 -0.364206 o -0.438 -0.899 0.488 251 o -0.946 -0.326 2.904 296 o -0.899 0.438 -2.050 341 o -0.326 0.946 -0.344207 o -0.454 -0.891 0.510 252 o -0.951 -0.309 3.078 297 o -0.891 0.454 -1.963 342 o -0.309 0.951 -0.325208 o -0.469 -0.883 0.532 253 o -0.956 -0.292 3.271 298 o -0.883 0.469 -1.881 343 o -0.292 0.956 -0.306209 o -0.485 -0.875 0.554 254 o -0.961 -0.276 3.487 299 o -0.875 0.485 -1.804 344 o -0.276 0.961 -0.287210 o -0.500 -0.866 0.577 255 o -0.966 -0.259 3.732 300 o -0.866 0.500 -1.732 345 o -0.259 0.966 -0.268211 o -0.515 -0.857 0.601 256 o -0.970 -0.242 4.011 301 o -0.857 0.515 -1.664 346 o -0.242 0.970 -0.249212 o -0.530 -0.848 0.625 257 o -0.974 -0.225 4.331 302 o -0.848 0.530 -1.600 347 o -0.225 0.974 -0.231213 o -0.545 -0.839 0.649 258 o -0.978 -0.208 4.705 303 o -0.839 0.545 -1.540 348 o -0.208 0.978 -0.213214 o -0.559 -0.829 0.675 259 o -0.982 -0.191 5.145 304 o -0.829 0.559 -1.483 349 o -0.191 0.982 -0.194215 o -0.574 -0.819 0.700 260 o -0.985 -0.174 5.671 305 o -0.819 0.574 -1.428 350 o -0.174 0.985 -0.176216 o -0.588 -0.809 0.727 261 o -0.988 -0.156 6.314 306 o -0.809 0.588 -1.376 351 o -0.156 0.988 -0.158217 o -0.602 -0.799 0.754 262 o -0.990 -0.139 7.115 307 o -0.799 0.602 -1.327 352 o -0.139 0.990 -0.141218 o -0.616 -0.788 0.781 263 o -0.993 -0.122 8.144 308 o -0.788 0.616 -1.280 353 o -0.122 0.993 -0.123219 o -0.629 -0.777 0.810 264 o -0.995 -0.105 9.514 309 o -0.777 0.629 -1.235 354 o -0.105 0.995 -0.105220 o -0.643 -0.766 0.839 265 o -0.996 -0.087 11.430 310 o -0.766 0.643 -1.192 355 o -0.087 0.996 -0.087221 o -0.656 -0.755 0.869 266 o -0.998 -0.070 14.301 311 o -0.755 0.656 -1.150 356 o -0.070 0.998 -0.070222 o -0.669 -0.743 0.900 267 o -0.999 -0.052 19.081 312 o -0.743 0.669 -1.111 357 o -0.052 0.999 -0.052223 o -0.682 -0.731 0.933 268 o -0.999 -0.035 28.636 313 o -0.731 0.682 -1.072 358 o -0.035 0.999 -0.035224 o -0.695 -0.719 0.966 269 o -1.000 -0.017 57.290 314 o -0.719 0.695 -1.036 359 o -0.017 1.000 -0.017225 o -0.707 -0.707 1.000 270 o -1.000 0.000 ##### 315 o -0.707 0.707 -1.000 360 o 0.000 1.000 0.000

TABEL SINUS, COSINUS, DAN TANGEN

Page 2 of 2 MGMP Fisika SMA Negeri 9 Kota Tangerang Selatanhttp://mgmpfisikasma9.wordpress.com

1Teorema Pythagoras

Teorema Pythagoras :

AB2 = AC2 + BC2

atau

c2 = a2 + b2

Apabila diketahui panjang dua sisi segitiga siku-siku, maka panjangsisi yang ketiga dapat dihitung dengan Teorema Pythagoras.

B

AC b

ac

2

Contoh Soal:Hitunglah panjang sisi x yang belum diketahui, padasegitiga siku-siku berikut ini :

125

x Jawab :x2 = 122 + 52

= 144 + 25= 169

x = 169 = 13

(a)

(b)

1943

x

Jawab :432 = x2 + 192x2 = 432 - 192

= 1849 361= 1488

x = 1488 = 38,57460 38,57

Teorema Pythagoras

3

CA

B

hipotenu

sa = sisi

miring

depan

samping

)

sin = =sisi depansisi miring

BC AB

cos = =sisi sampingsisi miring AC AB

tan = =sisi depansamping

BC AC

Perbandingan Trigonometri

Sinus, Cosinus dan Tangen

4

Hubungan perbandingan trigonometri segitiga siku-siku padakoordinat Cartesius ditunjukkan sbb. :

x

)

O A

B(x,y)

ry

x

y

sin = =sisi depansisi miring

y r

cos = =sisi sampingsisi miring

x r

tan = =sisi depansamping

y x


Catatan:Hubungan nilai sin dan besar sudut dapat dilihat pada tabel sinus

5

sec = = = 1 x r/x = 1

cos r x

csc = = = 1 x r/y = 1

sin r y

1 y/r

1 x/r

cot = = = 1 x x/y = 1

tan x y

1 y/x

Secan, Cosecan dan Cotangen (sec, csc dan cot)Perbandingan trigonometri selain sinus, cosinusdan tangen ada perbandingan yang lain, yaitusecan, cosecan dan cotangen.

x

)

O A

B(x,y)

ry

x

y


Perbandingan secan, cosecan dancotangen tersebut adalah sbb. :

6

sec = r x

cot = x y

csc = r y sin =

y r

tan = y x

cos = x r

sec kebalikan dari cos

csc kebalikan dari sin

cot kebalikan dari tan

x )

O A

B(x,y)

ry

x

y

Hubunganantara cos, sin, dan tan dengan sec, csc dan cot adalah kebalikannya.


7VEKTOR KOMPONENDAN

RESULTAN BEBERAPA VEKTOR

DENGAN PENDEKATAN

TRIGONOMETRI

8

F

VektorKomponen

X

Vektor KomponenF adalah:

Fx dan Fy.

Besar vektorkomponen.

Fx = F.cos Fy = F.sin

Y

Fy

Fx

Pen

deka

tan

Trig

onom

etri

9

360o90o90o

90o 90o

YKwadran I

Semua positif

Kwadran III

Tangen positifKwadran IV

Cosinus positif

Kwadran II

Sinus positif

X

Hubungan antarabesar sudut (), jari-jari (r), komponen x, dan komponen y.

Sinus sin =y/rCosinus cos=x/rTangen tan=y/x

r

Pen

deka

tan

Trig

onom

etri

10

F

Kwadran I

sem positif

Kwadran III

tan positifKwadran IV

cos positif

Kwadran II

sin positif

X

Fx = F.cos

Fy = F.sin

Y

Fy

Fx

Pen

deka

tan

Trig

onom

etri

11

F

Kwadran I

sem positif

Kwadran III


cos positif

Kwadran II

sin positif

X

Fx = F.cos

F.(-cos(180o-))

F.(-cos )

Fy = F.sin

F.sin(180o-)

F.sin

Y

Fy

Fx

Pen

deka

tan

Trig

onom

etri

12

F

Kwadran I

sem positif

Kwadran III


cos positif

Kwadran II

sin positif

X

Fx = F.cos

F.(-cos(-180o))

F.(-cos )

Fy = F.sin

F.(-sin(-180o))

F.(-sin )

Y

Fx

Fy

Pen

deka

tan

Trig

onom

etri

13

X

F

Kwadran I

sem positif

Kwadran III


cos positif

Kwadran II

sin positif

Fx = F.cos

F.cos(360o-)

F.cos

Fy = F.sin

F.(-sin(360o-))

F.(-sin )

Y

Fy

Fx

Pen

deka

tan

Trig

onom

etri

14

Sudut Istimewa

tan

cos

sin

sin/cos

1/201/211/221/231/24

1/241/231/221/211/20

90o60o45o30o0o

Pen

deka

tan

Trig

onom

etri

Untuk besar sudut yang lain (0o s/d 360o) lihat pada tabel !

15

FR

ResultanVektor

X

Y

Fy

Fx

Vektor Komponen FR.adalah Fx dan Fy.

Resultan VektorKomponen Fx dan Fyadalah FR.

Besarnya:FR2 = Fx2+Fy2

FR = Fx2+Fy2

Pen

deka

tan

Trig

onom

etri

16

F1

ResultanBeberapaVektor

X

Y Resultan darivektor F1, F2, F3, danF4 adalah FR.

Besar FR.FR2 = Fx2+ Fy2

FR = Fx2+ Fy2

Besar Fx dan Fy.Fx=F1x+F2x+F3x+F4xFy=F1y+F2y+F3y+F4y

F3

F2

F4

j

Pen

deka

tan

Trig

onom

etri

17

F1

ArahResultanVektor

X

YIngat!Besar FR :FR = Fx2+ Fy2

Arah FR :

tan = Fy / Fx

= . derajat(lihat tabel)

Jadi arah FR = derajat terhadapsumbu X positif.

F3

F2

F4

j

Pen

deka

tan

Trig

onom

etri

18

F1

Contoh Soal

X

YPerhatikan gambar disamping!Diketahui:F1=20 N, F2=25 N F3=30 N, F4=40 N, sedangkan besarsudutnya =60o, =30o, j=45o, =60o. Hitunglah:a.Komponen masing-

masing vektor.b.Besar Fx.c.Besar Fy.d.Besar FR e.Arah FR

F3

F2

F4

j

Pen

deka

tan

Trig

onom

etri

Documents

Tabel Sinus Plus3