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| This is a graphical construction of the various trigonometric functions from a chord AD (angle θ) of the unit circle centered at O.  In addition to the modern trigonometric functions sin (sine), cos (cosine), tan (tangent), cot (cotangent), sec (secant), and csc (cosecant), the diagram also includes a few trigonometric functions that have fallen into disuse: chord, versin (versine or versed sine), exsec (exsecant), cvs (coversine), and excsc (excosecant).| Eigenes Werk, basierend auf: Circle-trig6.png| Original: Steven G. Johnson in der Wikipedia auf Englisch Vektor: Limaner| [{Image src='https://www.austria-forum.org/cc/images/slim/by-sa.png' alt='CC BY-SA 3.0' align='center' link='https://www.austria-forum.org/cc/by-sa-30.html' target='_blank'}]| Datei:Circle-trig6.svg
| We have the unit circle (with radius = 1) in green, placed at the origin at the bottom right. In the middle of this circle, in yellow, is represented the angle theta (θ). This angle is the amount of counter-clockwise rotation around the circle starting from the right, on the x-axis, as illustrated. An exact copy of this little angle is shown at the top right, as a visual illustration of the definition of θ. At this angle, and starting at the origin, a (faint) green line is traced outwards, radially. This line intersects the unit circle at a single point, which is the green point spinning around at a constant rate as the angle θ changes, also at a constant rate. The vertical position of this point is projected straight (along the faint red line) onto the graph on the left of the circle. This results in the red point. The y-coordinate of this red point (the same as the y-coordinate of the green point) is the value of the sine function evaluated at the angle θ, that is: y coordinate of green point = sin θ As the angle θ changes, the red point moves up and down, tracing the red graph. This is the graph for the sine function. The faint vertical lines seen passing to the left are marking every quadrant along the circle, that is, at every angle of 90° or π/2 radians. Notice how the sine curve goes from 1, to zero, to -1, then back to zero, at exactly these lines. This is reflecting the fact sin(0) = 0, sin(π/2) =1, sin(π) = 0 and sin(3π/ 2) -1 A similar process is done with the x-coordinate of the green point. However, since the x-coordinate is tilted from the usual convention to plot graphs (where y = f(x), with y vertical and x horizontal), an “untilt” operation was performed in order to repeat the process again in the same orientation, instead of vertically. This was represented by a “bend”, seen on the top right. Again, the green point is projected upwards (along the faint blue line) and this “bent” projection ends up in the top graph’s rightmost edge, at the blue point. The y-coordinate of this blue point (which, due to the “bend” in the projection, is the same as the x-coordinate of the green point) is the value of the cosine function evaluated at the angle θ, that is: x coordinate of green point = cos θ The blue curve traced by this point, as it moves up and down with changing θ, is the the graph of the cosine function. Notice again how it behaves at it crosses every quadrant, reflecting the fact cos(0) = 1, cos(π/2) = 0, cos(π) = -1 and cos(3π/2) = 0.| Eigenes Werk| Lucas Vieira| [{Image src='https://www.austria-forum.org/cc/images/slim/publicdomain.png' alt='Public domain' align='center' link='https://www.austria-forum.org/cc/public-domain-10.html' target='_blank'}]| Datei:Circle cos sin.gif
| The Wikimedia Commons logo, SVG version.| Original created by Reidab ( PNG version ) SVG version was created by Grunt and cleaned up by 3247 . Re-creation with SVG geometry features by Pumbaa , using a proper partial circle and SVG geometry features. (Former versions used to be slightly warped.)| Reidab , Grunt , 3247 , Pumbaa| [{Image src='https://www.austria-forum.org/cc/images/slim/by-sa.png' alt='CC BY-SA 3.0' align='center' link='https://www.austria-forum.org/cc/by-sa-30.html' target='_blank'}]| Datei:Commons-logo.svg
| Plot of all six trigonometric functions in the interval -2π,2π: y 1 ( x ) = arcsin( x ) y 2 ( x ) = arccos( x ) y 3 ( x ) = arctan( x ) y 4 ( x ) = arccot( x ) y 5 ( x ) = arcsec( x ) y 6 ( x ) = arccsc( x )| Eigenes Werk| Geek3| [{Image src='https://www.austria-forum.org/cc/images/slim/by.png' alt='CC BY 3.0' align='center' link='https://www.austria-forum.org/cc/by-30.html' target='_blank'}]| Datei:Mplwp trigonometric functions piaxis.svg
| Rechtwinkliges Dreieck| http://de.wikipedia.org/wiki/Bild:RechtwinkligesDreieck.svg| PaterSigmund (Original by Cweiske)| [{Image src='https://www.austria-forum.org/cc/images/slim/by-sa.png' alt='CC BY-SA 2.5' align='center' link='https://www.austria-forum.org/cc/by-sa-25.html' target='_blank'}]| Datei:RechtwinkligesDreieck.svg
| Die Trigonometrischen Funktionen am Einheitskreis: C P ¯ = sin ⁡ b \displaystyle \overline CP=\sin b S P ¯ = cos ⁡ b \displaystyle \overline SP=\cos b D T ¯ = tan ⁡ b \displaystyle \overline DT=\tan b E K ¯ = cot ⁡ b \displaystyle \overline EK=\cot b O T ¯ = sec b \displaystyle \overline OT=\operatorname sec \,b O K ¯ = csc b \displaystyle \overline OK=\operatorname csc \,b| Eigenes Werk| MartinThoma| [{Image src='https://www.austria-forum.org/cc/images/slim/cc-zero.png' alt='CC0' align='center' link='https://www.austria-forum.org/cc/cc0-10.html' target='_blank'}]| Datei:Trigonomatric-functions.svg
| Grafische Veranschaulichung der Ungleichung von Aristarchos| Eigenes Werk| Mabit1| [{Image src='https://www.austria-forum.org/cc/images/slim/by-sa.png' alt='CC BY-SA 4.0' align='center' link='https://www.austria-forum.org/cc/by-sa-40.html' target='_blank'}]| Datei:Ungleichung von Aristarchos.svg
| Die Winkelfunktionen im Einheitskreis.| Eigenes Werk| TheCarnil| [{Image src='https://www.austria-forum.org/cc/images/slim/publicdomain.png' alt='Public domain' align='center' link='https://www.austria-forum.org/cc/public-domain-10.html' target='_blank'}]| Datei:Winkelfunktionen Einheitskreis.svg
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