Fil:Unit circle angles.svg
Hopp til navigering
Hopp til søk
Størrelse for denne PNG-forhåndsvisningen av denne SVG-filen: 600 × 600 piksler Andre oppløsninger: 240 × 240 piksler | 480 × 480 piksler | 768 × 768 piksler | 1 024 × 1 024 piksler | 2 048 × 2 048 piksler | 720 × 720 piksler.
Opprinnelig fil (SVG-fil, standardstørrelse 720 × 720 piksler, filstørrelse: 238 KB)
Beskrivelse
| Beskrivelse |
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. |
| Dato | |
| Kilde | Own work using: Eukleides |
| Opphavsperson | Gustavb (diskusjon · bidrag) |
| Andre versjoner |
Derivative works of this file: Unit circle angles color.svg:  |
| SVG utvikling |  Denne vektorgrafikken ble laget med Other tools. |
Lisensiering
|
This image of simple geometry is ineligible for copyright and therefore in the public domain, because it consists entirely of information that is common property and contains no original authorship. |  |
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
|
|---|
|
Filhistorikk
Klikk på et tidspunkt for å vise filen slik den var på det tidspunktet.
| Dato/klokkeslett | Miniatyrbilde | Dimensjoner | Bruker | Kommentar | |
|---|---|---|---|---|---|
| nåværende | 4. mar. 2011 kl. 21:33 | | 720 × 720 (238 KB) | wikimediacommons>Tryphon | Valid SVG. |
Filbruk
Det er ingen sider som bruker denne filen.
