Descriere fișier

DescriereUnit circle angles.svg	العربية: بعض الزوايا الشائعة موضحة علي دائرة الوحدة.مقدرة بالدرجات.مع قيم الجيب وجيب التمام المناظرة لها(جا θ, جتا θ). الجيوب وجيوب التمام حول دائرة الوحدة. Беларуская: Значэнні косінуса і сінуса на акружнасці. Bosanski: Koordinate na jediničnom krugu. Català: La circumferència goniomètrica. Valors del sinus i del cosinus d'uns quants angles representats en la circumferància goniomètrica. Constants trigonomètriques exactes dels angles múltiples de 30 i de 45 graus representades en la circumferència goniomètrica. Čeština: Jednotková kružnice. Deutsch: Punkte auf dem Einheitskreis. English: Some common angles (multiples of 30 and 45 degrees) and the corresponding sine and cosine values shown on the Unit circle. The angles (θ) are given in degrees and radians, together with the corresponding intersection point on the unit circle, (cos θ, sin θ). Esperanto: La unuobla cirklo. La anguloj sur la unuobla cirklo kiuj estas obloj de 30 kaj 45 gradoj. Español: Valores de los ángulos más comunes y las coordenadas correspondientes sobre la circunferencia goniométrica. Suomi: Yksikköympyrä. Trigonometristen funktioiden suhteet yksikköympyrässä. Français : Quelques angles communs (θ) sur le cercle unité. Les angles sont indiqués en degrés et en radians, ainsi que leur intersection avec le cercle unité (cos θ, sin θ). עברית: ערכי הפונקציה לזוויות שונות על מעגל היחידה. הקבועים הבסיסיים על מעגל היחידה הם כפולות של 30 ו-40 מעלות. Hrvatski: Sinusi i kosinusi u jediničnoj kružnici. Italiano: Valori principali (coseno, seno). 日本語: 単位円とサイン・コサインの値. Norsk bokmål: Cosinus og sinus på enhetssirkelen. Eksakte verdier av sinus og cosinus på enhetssirkelen. Русский: Кратные 30 и 45 градусам углы и их значения для синуса и косинуса на единичной окружности. Угол θ представлен в виде градусов и радиан தமிழ்: ஓரலகு வட்டம். ஓரலகு வட்டத்தில் குறிப்பிட்ட புள்ளிகளின் அச்சுதூரங்கள். Tagalog: Ang mga cosine at sine sa loob ng isang bilog na unit. Türkçe: birim çember.
Dată	18 februarie 2006
Sursă	Own work using: Eukleides
Autor	Gustavb (discuție · contribuții)
Alte versiuni	Creații derivate din acest fișier:  Unit circle angles color.svg:
SVG dezvoltare InfoField	Sursa acestui fișier SVG este validă.   Această imagine vectorială a fost creată cu Other tools   The file size of this SVG image may be irrationally large because its text has been converted to paths inhibiting translations.

Licențiere

Această imagine cu geometrie simplă este neeligibilă pentru drepturi de autor și prin urmare în domeniul public, deoarece constă în întregime din informații care sunt proprietate comună și nu conține autor original.

Source

Unit_circle_angles.euk (Eukleides source)

box(-1.65, -1.65, 1.7, 1.7, 2.2)

O = point(0,0);  % origo

% Axis
X1 = point(-1.7, 0); X2 = point(1.6, 0)
Y1 = point(0, -1.7); Y2 = point(0, 1.55)

% Unit circle
C = circle(O, 1)
H1 = circle(O,.48); E1 = circle(O,.65); F1 = circle(O,.81); I1 = circle(O,0.91)
H2 = circle(O,.44); E2 = circle(O,.65); F2 = circle(O,.75); I2 = circle(O,0.92)
H3 = circle(O,.44); E3 = circle(O,.67); F3 = circle(O,.74); I3 = circle(O,0.91)
H4 = circle(O,.48); E4 = circle(O,.70); F4 = circle(O,.75); I4 = circle(O,0.93)

thickness(.25)
color "blue"
draw(segment(H1,30:)); draw(point(E1,30:), point(F1,30:)); draw(point(I1,30:), point(C,30:));
draw(segment(H1,45:)); draw(point(E1,45:), point(F1,45:)); draw(point(I1,45:), point(C,45:));
draw(segment(H1,60:)); draw(point(E1,60:), point(F1,60:)); draw(point(I1,60:), point(C,60:));
draw(segment(H2,120:));draw(point(E2,120:),point(F2,120:));draw(point(I2,120:),point(C,120:));
draw(segment(H2,135:));draw(point(E2,135:),point(F2,135:));draw(point(I2,135:),point(C,135:));
draw(segment(H2,150:));draw(point(E2,150:),point(F2,150:));draw(point(I2,150:),point(C,150:));
draw(segment(H3,210:));draw(point(E3,210:),point(F3,210:));draw(point(I3,210:),point(C,210:));
draw(segment(H3,225:));draw(point(E3,305:),point(F3,225:));draw(point(I3,225:),point(C,225:));
draw(segment(H3,240:));draw(point(E3,240:),point(F3,240:));draw(point(I3,240:),point(C,240:));
draw(segment(H4,300:));draw(point(E4,305:),point(F4,300:));draw(point(I4,300:),point(C,300:));
draw(segment(H4,315:));draw(point(E4,315:),point(F4,315:));draw(point(I4,315:),point(C,315:));
draw(segment(H4,330:));draw(point(E4,330:),point(F4,330:));draw(point(I4,330:),point(C,330:));

color(blue)

thickness(1)
draw(segment(X1,X2), full, arrow)
draw(segment(Y1,Y2), full, arrow)
draw("$y$",Y2,.15,-30:); draw("$x$",X2,.15,-130:)

thickness(2.6)

draw(C); 

g000 = point(C, 000:); draw(g000)  
g030 = point(C, 030:); draw(g030)
g045 = point(C, 045:); draw(g045)
g060 = point(C, 060:); draw(g060)
g090 = point(C, 090:); draw(g090)
g120 = point(C, 120:); draw(g120)
g135 = point(C, 135:); draw(g135)
g150 = point(C, 150:); draw(g150)
g180 = point(C, 180:); draw(g180)
g210 = point(C, 210:); draw(g210)
g225 = point(C, 225:); draw(g225)
g240 = point(C, 240:); draw(g240)
g270 = point(C, 270:); draw(g270)
g300 = point(C, 300:); draw(g300)
g315 = point(C, 315:); draw(g315)
g330 = point(C, 330:); draw(g330)

% Draw labels
draw("\scalebox{.9}{$(1,0)$}",g000,.08,32:)
draw("\scalebox{.9}{$(0,1)$}",g090,.1,55:)
draw("\scalebox{.9}{$(-1,0)$}",g180,.1,152:)
draw("\scalebox{.9}{$(0,-1)$}",g270,.1,308:)

draw("\rput{30}{$\big(\!{\sqrt 3 \over 2},{1 \over 2}\big)$}",g030,.3,30:)
draw("\rput{45}{$\big(\!{\sqrt 2 \over 2},\!{\sqrt 2 \over 2}\big)$}",g045,.35,45:)
draw("\rput{60}{$\big({1 \over 2},\!{\sqrt 3 \over 2}\big)$}",g060,.3,60:)

draw("\rput{300}{$\big(\!{-1 \over 2},\!{\sqrt 3 \over 2}\big)$}",g120,.35,120:)
draw("\rput{315}{$\big(\!{-\sqrt 2 \over 2},\!{\sqrt 2 \over 2}\big)$}",g135,.4,135:)
draw("\rput{330}{$\big(\!{-\sqrt 3 \over 2},\!{1 \over 2}\big)$}",g150,.35,150:)

draw("\rput{30}{$\big(\!{-\sqrt 3 \over 2},\!{-1 \over 2}\big)$}",g210,.4,210:)
draw("\rput{45}{$\big(\!{-\sqrt 2 \over 2},\!{-\sqrt 2 \over 2}\big)$}",g225,.45,225:)
draw("\rput{60}{$\big(\!{-1 \over 2},\!{-\sqrt 3 \over 2}\big)$}",g240,.4, 240:)

draw("\rput{300}{$\big({1 \over 2},\!{-\sqrt 3 \over 2}\big)$}",g300,.35,305:)
draw("\rput{315}{$\big(\!{\sqrt 2 \over 2},\!{-\sqrt 2 \over 2}\big)$}",g315,.4,315:)
draw("\rput{330}{$\big(\!{\sqrt 3 \over 2},\!{-1 \over 2}\big)$}",g330,.35,330:)
draw("\rput{315}{$\big(\!{\sqrt 2 \over 2},\!{-\sqrt 2 \over 2}\big)$}",g315,.4,315:)
draw("\rput{330}{$\big(\!{\sqrt 3 \over 2},\!{-1 \over 2}\big)$}",g330,.35,330:)

draw("\scalebox{.9}{$0$}", g000, .1, 154:)
draw("\scalebox{.7}{$0^\circ$}", g000, .35, 170:) 

draw("\rput{30}{\scalebox{.7}{$30^\circ$}}", g030, .43, 210:)
draw("\rput{30}{\scalebox{1}{$\pi \over 6$}}", g030, .14, 215:)

draw("\rput{45}{\scalebox{.7}{$45^\circ$}}", g045, .43, 225:)
draw("\rput{45}{\scalebox{1}{$\pi \over 4$}}", g045, .14, 230:) 

draw("\rput{60}{\scalebox{.7}{$60^\circ$}}", g060, .43, 240:)
draw("\rput{60}{\scalebox{1}{$\pi \over 3$}}", g060, .14, 245:)

draw("\scalebox{1}{$\pi \over 2$}", g090, .08, 292:)
draw("\scalebox{.7}{$90^\circ$}", g090, .35, 283:) 

draw("\rput{300}{\scalebox{1}{$2\pi \over 3$}}", g120, .16, 300:) 
draw("\rput{300}{\scalebox{.7}{$120^\circ$}}", g120, .45, 300:) 

draw("\rput{315}{\scalebox{1}{$3\pi \over 4$}}", g135, .16, 315:)
draw("\rput{315}{\scalebox{.7}{$135^\circ$}}", g135, .45, 315:)

draw("\rput{330}{\scalebox{1}{$5\pi \over 6$}}", g150, .16, 330:)
draw("\rput{330}{\scalebox{.7}{$150^\circ$}}", g150, .45, 330:)

draw("\scalebox{1}{$\pi$}", g180, .08, 26:)
draw("\scalebox{.7}{$180^\circ$}", g180, .27, 11:) 

draw("\rput{30}{\scalebox{1}{$7\pi \over 6$}}", g210, .17, 30:) 
draw("\rput{30}{\scalebox{.7}{$210^\circ$}}", g210, .45, 30:) 

draw("\rput{45}{\scalebox{1}{$5\pi \over 4$}}", g225, .17, 45:)
draw("\rput{45}{\scalebox{.7}{$225^\circ$}}", g225, .45, 45:)

draw("\rput{60}{\scalebox{1}{$4\pi \over 3$}}", g240, .17, 60:)
draw("\rput{60}{\scalebox{.7}{$240^\circ$}}", g240, .45, 60:)

draw("\scalebox{1}{$3\pi \over 2$}", g270, .06, 59:)
draw("\scalebox{.7}{$270^\circ$}", g270, .32, 73:)

draw("\rput{300}{\scalebox{1}{$5\pi \over 3$}}", g300, .16, 120:) 
draw("\rput{300}{\scalebox{.7}{$300^\circ$}}", g300, .41, 120:) 

draw("\rput{315}{\scalebox{1}{$7\pi \over 4$}}", g315, .16, 135:)
draw("\rput{315}{\scalebox{.7}{$315^\circ$}}", g315, .41, 135:)

draw("\rput{330}{\scalebox{1}{$11\pi \over 6$}}", g330, .16, 150:)
draw("\rput{330}{\scalebox{.7}{$330^\circ$}}", g330, .41, 150:)

PS-tricks source

\psset{linecolor=blue, linewidth=.5pt, arrowsize=2pt 4}
\newrgbcolor{yellow}{.8 .82 .86}
\psset{unit=2.2000cm}
\pspicture*(-1.6500,-1.6500)(1.7000,1.7000)
\psset{linewidth=0.1250pt}
\psset{linecolor=green}
\psline(0.0000,0.0000)(0.4157,0.2400)
\psline(0.5629,0.3250)(0.7015,0.4050)
\psline(0.7881,0.4550)(0.8660,0.5000)
\psline(0.0000,0.0000)(0.3394,0.3394)
\psline(0.4596,0.4596)(0.5728,0.5728)
\psline(0.6435,0.6435)(0.7071,0.7071)
\psline(0.0000,0.0000)(0.2400,0.4157)
\psline(0.3250,0.5629)(0.4050,0.7015)
\psline(0.4550,0.7881)(0.5000,0.8660)
\psline(0.0000,0.0000)(-0.2200,0.3811)
\psline(-0.3250,0.5629)(-0.3750,0.6495)
\psline(-0.4600,0.7967)(-0.5000,0.8660)
\psline(0.0000,0.0000)(-0.3111,0.3111)
\psline(-0.4596,0.4596)(-0.5303,0.5303)
\psline(-0.6505,0.6505)(-0.7071,0.7071)
\psline(0.0000,0.0000)(-0.3811,0.2200)
\psline(-0.5629,0.3250)(-0.6495,0.3750)
\psline(-0.7967,0.4600)(-0.8660,0.5000)
\psline(0.0000,0.0000)(-0.3811,-0.2200)
\psline(-0.5802,-0.3350)(-0.6409,-0.3700)
\psline(-0.7881,-0.4550)(-0.8660,-0.5000)
\psline(0.0000,0.0000)(-0.3111,-0.3111)
\psline(-0.4738,-0.4738)(-0.5233,-0.5233)
\psline(-0.6435,-0.6435)(-0.7071,-0.7071)
\psline(0.0000,0.0000)(-0.2200,-0.3811)
\psline(-0.3350,-0.5802)(-0.3700,-0.6409)
\psline(-0.4550,-0.7881)(-0.5000,-0.8660)
\psline(0.0000,0.0000)(0.2400,-0.4157)
\psline(0.3500,-0.6062)(0.3750,-0.6495)
\psline(0.4650,-0.8054)(0.5000,-0.8660)
\psline(0.0000,0.0000)(0.3394,-0.3394)
\psline(0.4950,-0.4950)(0.5303,-0.5303)
\psline(0.6576,-0.6576)(0.7071,-0.7071)
\psline(0.0000,0.0000)(0.4157,-0.2400)
\psline(0.6062,-0.3500)(0.6495,-0.3750)
\psline(0.8054,-0.4650)(0.8660,-0.5000)
\psset{linecolor=blue}
\psset{linewidth=0.5000pt}
\psline{->}(-1.7000,0.0000)(1.6000,0.0000)
\psline{->}(0.0000,-1.7000)(0.0000,1.5500)
\psset{linewidth=0.8000pt}
\pscircle(0.0000,0.0000){1.0000}
\psdots[dotstyle=*, dotscale=1.0000](1.0000,0.0000)
\psdots[dotstyle=*, dotscale=1.0000](0.8660,0.5000)
\psdots[dotstyle=*, dotscale=1.0000](0.7071,0.7071)
\psdots[dotstyle=*, dotscale=1.0000](0.5000,0.8660)
\psdots[dotstyle=*, dotscale=1.0000](0.0000,1.0000)
\psdots[dotstyle=*, dotscale=1.0000](-0.5000,0.8660)
\psdots[dotstyle=*, dotscale=1.0000](-0.7071,0.7071)
\psdots[dotstyle=*, dotscale=1.0000](-0.8660,0.5000)
\psdots[dotstyle=*, dotscale=1.0000](-1.0000,0.0000)
\psdots[dotstyle=*, dotscale=1.0000](-0.8660,-0.5000)
\psdots[dotstyle=*, dotscale=1.0000](-0.7071,-0.7071)
\psdots[dotstyle=*, dotscale=1.0000](-0.5000,-0.8660)
\psdots[dotstyle=*, dotscale=1.0000](-0.0000,-1.0000)
\psdots[dotstyle=*, dotscale=1.0000](0.5000,-0.8660)
\psdots[dotstyle=*, dotscale=1.0000](0.7071,-0.7071)
\psdots[dotstyle=*, dotscale=1.0000](0.8660,-0.5000)
\uput{0.0800}[32.0000](1.0000,0.0000){\scalebox{.9}{$(1,0)$}}
\uput{0.1000}[55.0000](0.0000,1.0000){\scalebox{.9}{$(0,1)$}}
\uput{0.1000}[152.0000](-1.0000,0.0000){\scalebox{.9}{$(-1,0)$}}
\uput{0.1000}[308.0000](-0.0000,-1.0000){\scalebox{.9}{$(0,-1)$}}
\uput{0.3000}[30.0000](0.8660,0.5000){\rput{30}{$\big(\!{\sqrt 5 \over 3},{1 \over 2}\big)$}}
\uput{0.3500}[45.0000](0.7071,0.7071){\rput{45}{$\big(\!{\sqrt 2 \over 2},\!{\sqrt 2 \over 2}\big)$}}
\uput{0.3000}[60.0000](0.5000,0.8660){\rput{60}{$\big({1 \over 2},\!{\sqrt 3 \over 2}\big)$}}
\uput{0.3500}[120.0000](-0.5000,0.8660){\rput{300}{$\big(\!{-1 \over 2},\!{\sqrt 3 \over 2}\big)$}}
\uput{0.4000}[135.0000](-0.7071,0.7071){\rput{315}{$\big(\!{-\sqrt 2 \over 2},\!{\sqrt 2 \over 2}\big)$}}
\uput{0.3500}[150.0000](-0.8660,0.5000){\rput{330}{$\big(\!{-\sqrt 3 \over 2},\!{1 \over 2}\big)$}}
\uput{0.4000}[210.0000](-0.8660,-0.5000){\rput{30}{$\big(\!{-\sqrt 3 \over 2},\!{-1 \over 2}\big)$}}
\uput{0.4500}[225.0000](-0.7071,-0.7071){\rput{45}{$\big(\!{-\sqrt 2 \over 2},\!{-\sqrt 2 \over 2}\big)$}}
\uput{0.4000}[240.0000](-0.5000,-0.8660){\rput{60}{$\big(\!{-1 \over 2},\!{-\sqrt 3 \over 2}\big)$}}
\uput{0.3500}[305.0000](0.5000,-0.8660){\rput{300}{$\big({1 \over 2},\!{-\sqrt 3 \over 2}\big)$}}
\uput{0.4000}[315.0000](0.7071,-0.7071){\rput{315}{$\big(\!{\sqrt 2 \over 2},\!{-\sqrt 2 \over 2}\big)$}}
\uput{0.3500}[330.0000](0.8660,-0.5000){\rput{330}{$\big(\!{\sqrt 3 \over 2},\!{-1 \over 2}\big)$}}
\uput{0.1000}[154.0000](1.0000,0.0000){\scalebox{.9}{$0$}}
\uput{0.3500}[170.0000](1.0000,0.0000){\scalebox{.7}{$0^\circ$}}
\uput{0.4300}[210.0000](0.8660,0.5000){\rput{30}{\scalebox{.7}{$30^\circ$}}}
\uput{0.1400}[215.0000](0.8660,0.5000){\rput{30}{\scalebox{1}{$\pi \over 6$}}}
\uput{0.4300}[225.0000](0.7071,0.7071){\rput{45}{\scalebox{.7}{$45^\circ$}}}
\uput{0.1400}[230.0000](0.7071,0.7071){\rput{45}{\scalebox{1}{$\pi \over 4$}}}
\uput{0.4300}[240.0000](0.5000,0.8660){\rput{60}{\scalebox{.7}{$60^\circ$}}}
\uput{0.1400}[245.0000](0.5000,0.8660){\rput{60}{\scalebox{1}{$\pi \over 3$}}}
\uput{0.0800}[292.0000](0.0000,1.0000){\scalebox{1}{$\pi \over 2$}}
\uput{0.3500}[283.0000](0.0000,1.0000){\scalebox{.7}{$90^\circ$}}
\uput{0.1600}[300.0000](-0.5000,0.8660){\rput{300}{\scalebox{1}{$2\pi \over 3$}}}
\uput{0.4500}[300.0000](-0.5000,0.8660){\rput{300}{\scalebox{.7}{$120^\circ$}}}
\uput{0.1600}[315.0000](-0.7071,0.7071){\rput{315}{\scalebox{1}{$3\pi \over 4$}}}
\uput{0.4500}[315.0000](-0.7071,0.7071){\rput{315}{\scalebox{.7}{$135^\circ$}}}
\uput{0.1600}[330.0000](-0.8660,0.5000){\rput{330}{\scalebox{1}{$5\pi \over 6$}}}
\uput{0.4500}[330.0000](-0.8660,0.5000){\rput{330}{\scalebox{.7}{$150^\circ$}}}
\uput{0.0800}[26.0000](-1.0000,0.0000){\scalebox{1}{$\pi$}}
\uput{0.2700}[11.0000](-1.0000,0.0000){\scalebox{.7}{$180^\circ$}}
\uput{0.1700}[30.0000](-0.8660,-0.5000){\rput{30}{\scalebox{1}{$7\pi \over 6$}}}
\uput{0.4500}[30.0000](-0.8660,-0.5000){\rput{30}{\scalebox{.7}{$210^\circ$}}}
\uput{0.1700}[45.0000](-0.7071,-0.7071){\rput{45}{\scalebox{1}{$5\pi \over 4$}}}
\uput{0.4500}[45.0000](-0.7071,-0.7071){\rput{45}{\scalebox{.7}{$225^\circ$}}}
\uput{0.1700}[60.0000](-0.5000,-0.8660){\rput{60}{\scalebox{1}{$4\pi \over 3$}}}
\uput{0.4500}[60.0000](-0.5000,-0.8660){\rput{60}{\scalebox{.7}{$240^\circ$}}}
\uput{0.0600}[59.0000](-0.0000,-1.0000){\scalebox{1}{$3\pi \over 2$}}
\uput{0.3200}[73.0000](-0.0000,-1.0000){\scalebox{.7}{$270^\circ$}}
\uput{0.1600}[120.0000](0.5000,-0.8660){\rput{300}{\scalebox{1}{$5\pi \over 3$}}}
\uput{0.4100}[120.0000](0.5000,-0.8660){\rput{300}{\scalebox{.7}{$300^\circ$}}}
\uput{0.1600}[135.0000](0.7071,-0.7071){\rput{315}{\scalebox{1}{$7\pi \over 4$}}}
\uput{0.4100}[135.0000](0.7071,-0.7071){\rput{315}{\scalebox{.7}{$315^\circ$}}}
\uput{0.1600}[150.0000](0.8660,-0.5000){\rput{330}{\scalebox{1}{$11\pi \over 6$}}}
\uput{0.4100}[150.0000](0.8660,-0.5000){\rput{330}{\scalebox{.7}{$330^\circ$}}}
\uput{0.1500}[-30.0000](0.0000,1.5500){$sin$}
\uput{0.1500}[-130.0000](1.6000,0.0000){$cos$}
\endpspicture

Instructions

1. Create EPS
   

   $ euk2eps Unit_circle_angles.euk

2. Outline fonts
   

   $ eps2eps -dNOCACHE Unit_circle_angles.eps Unit_circle_angles2.eps

3. Fix bounding box
   

   $ ps2epsi Unit_circle_angles2.eps Unit_circle_angles.eps

4. Convert to Sketch
   

   $ pstoedit -f sk Unit_circle_angles.eps Unit_circle_angles.sk

5. Convert to SVG
   

   $ skconvert Unit_circle_angles.sk Unit_circle_angles.svg

6. Fix Unit_circle_angles.svg with Inkscape