Sammanfattning

BeskrivningUnit 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.
Datum	18 februari 2006
Källa	Eget arbete med hjälp av: Eukleides
Skapare	Gustavb (diskussion · bidrag)
Andra versioner	Filer som bygger på denna fil:  Unit circle angles color.svg:
SVG utveckling InfoField	Källkoden till denna SVG är giltig.   Den här vektorbilden skapades med Other tools   The file size of this SVG image may be irrationally large because its text has been converted to paths inhibiting translations.

Licensiering

Den här bilden består endast av enkel geometri och kan inte upphovsrättsskyddas, eftersom den enbart består av information som är allmän egendom och saknar upphovsrättslig källa.

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