amplitude and phase shift in the 4 quadrants of the coefficient plane
for a sinusoidal 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HY8!#77$$!0ME5>//u"!#9$!0\(\r1#RS"!#97$$!06q(\2(ep"!#9$!0<H6i-uX"!#97$$!0&*)fsTlZ;!#9$!0x/bh*p6:!#97$$!0\q.bW=g"!#9$!00!)pLe,c"!#97$$!0>tG'o$3b"!#9$!0^c,*3(3h"!#97$$!0')oZ)e:'\"!#9$!0RbUW"yh;!#97$$!0lOA!R>Z9!#9$!0msS!3f/<!#97$$!/#zepRHR"!#8$!0;Z"\_?\<!#97$$!03Ee)oWN8!#9$!0_ge4$[$z"!#97$$!0.fh"*RyF"!#9$!0i^Bzs\$=!#97$$!0C&Gmb(3A"!#9$!0kW(RgNt=!#97$$!0*GHy*yi:"!#9$!/k&G\,R">!#87$$!0k\&>l3(4"!#9$!0GL&pbV[>!#97$$!0T%f_)\F."!#9$!02z_5(G$)>!#97$$!0U&HlN%\t*!#:$!0dW&3Z.8?!#97$$!0-<3P\t2*!#:$!0RrGfIN/#!#97$$!0/K*o:))\%)!#:$!0%3TzWEq?!#97$$!0lify-cy(!#:$!0p'=y(\h4#!#97$$!04;8`#\Gr!#:$!0d+Ba(R>@!#97$$!0FlM=[JV'!#:$!0'H\.*G:9#!#97$$!0*erEN'pv&!#:$!0iN!\#)og@!#97$$!0-oEb!ff]!#:$!/J$**yt!y@!#87$$!0d%)y$y#GO%!#:$!0/0r4$4$>#!#97$$!0=\f2]'=P!#:$!0@A_-I\?#!#97$$!0>)*y<fk(H!#:$!0")Q@Uph@#!#97$$!0`"=')zw4B!#:$!0W6*)\1TA#!#97$$!0Y*y>ql'f"!#:$!0j@UDg.B#!#97$$!0r(RmQwD"*!#;$!01KP,0UB#!#97$$!/Ajnf;?:!#:$!0l0NI;gB#!#97$$"0)*QQbiu1&!#;$!0f2**p$\NA!#97$$"0VCI)Q)QD"!#:$!0:xzg\DB#!#97$$"0NVx)*=O$>!#:$!0rQV*=pFA!#97$$"0T$**QJ1vE!#:$!0dzF44+A#!#97$$"0OA#y^W7L!#:$!0&>U&3(R6A!#97$$"0wakR")\.%!#:$!0*oq+6O*>#!#97$$"0O5(pF")GZ!#:$!0[rQ$Q\&=#!#97$$"0W#*z(3Y<a!#:$!//)*4&\%p@!#87$$"02-2/*=)4'!#:$!0u#*)*y18:#!#97$$"0L-66jku'!#:$!/inKf'=8#!#87$$"0`dco%HSu!#:$!0))3Wj`'3@!#97$$"0T9qzjT4)!#:$!0ml#3#HW3#!#97$$"0xr^,<Qx)!#:$!0nf$H`uc?!#97$$"0$>-ao$4Q*!#:$!0hZ[Wt(H?!#97$$"0*4RejA/5!#9$!0y%)HB")y*>!#97$$"0^*p2dbm5!#9$!0hy+&RJl>!#97$$"0DqpH#oF6!#9$!0")R%z!*)3$>!#97$$"09<W8V.>"!#9$!0i8VQ.H*=!#97$$"0o"Qbn#pC"!#9$!0^e@!z6c=!#97$$"0slGK)p.8!#9$!0c>nB#p;=!#97$$"0\:oxJ\O"!#9$!0#**oso9r<!#97$$"/c!H:/!>9!#8$!0tV+CG"G<!#97$$"0OYOW,HZ"!#9$!0i\g@FCo"!#97$$"0@#oTY?E:!#9$!0*4@guAM;!#97$$"0bX%e9"Qd"!#9$!0GE7SK%)e"!#97$$"0dHhSXIi"!#9$!0e<x*34Q:!#97$$"0"G\RNJq;!#9$!0-cFfCm["!#97$$"0U[\')o!><!#9$!0%=#p"e'*H9!#97$$"0k6"*[*\g<!#9$!0U!zpvjy8!#97$$"0Xmc/'R1=!#9$!0>$\jw#zJ"!#97$$"0rI1J>g%=!#9$!0zm26H=E"!#97$$"0lv5]5N)=!#9$!/Bz#p]^?"!#87$$"0ASj`$)=#>!#9$!0&>QtE'H9"!#97$$"0#)zSwY$e>!#9$!0<Wz6&Hz5!#97$$"0()f^,#p*)>!#9$!0lQemb.-"!#97$$"/wP+r.@?!#8$!0pCl2,xc*!#:7$$"07z1^o'\?!#9$!0P\'H7*y$*)!#:7$$"0Z(eq")[y?!#9$!0-'=.c_X#)!#:7$$"0oU/bR:5#!#9$!0c&yqM#*Qw!#:7$$"0YiD)*He7#!#9$!0mYXS7V$p!#:7$$"/QRP6^Y@!#8$!0-F9t,\E'!#:7$$"/#3Cm:\;#!#8$!0C;0"H*ef&!#:7$$"0*)H$exC"=#!#9$!0@fWRd4#\!#:7$$"0fk4RQd>#!#9$!0N#y:;oFU!#:7$$"0Jqv(Gp3A!#9$!0_q$\a?)[$!#:7$$"0zNNC$Q=A!#9$!0u%)4U-n!G!#:7$$"03&[Cq)eA#!#9$!0%\t$**f88#!#:7$$"0e$fe_jJA!#9$!0$f6M%psS"!#:7$$"0>nSzB]B#!#9$!0)y1cYuKo!#;7$$"0z*\xz1OA!#9$"/UJM3]M=!#A-%&COLORG6&%$RGBG$"#5!""$""!!""$""!!""-%'CURVESG6$7)7$$""!!""$""!!""7$$"#?!""$"#5!""7$$"#?!""$!#5!""7$$""!!""$""!!""7$$!#?!""$"#5!""7$$!#?!""$!#5!""7$$""!!""$""!!""-%&COLORG6&%$RGBG$"#5!""$""!!""$""!!""-%'CURVESG6%7&7$$"#?!""$"#5!""7$$"#?!""$!#5!""7$$!#?!""$"#5!""7$$!#?!""$!#5!""-%&COLORG6&%$RGBG$""!!""$""!!""$""!!""-%&STYLEG6#%&POINTG-&%&_AXISG6#"""6'-%+_GRIDLINESG6'-%&COLORG6&%$RGBG$""!!""$""!!""$""!!""-%*LINESTYLEG6#""!-%*THICKNESSG6#"""-%-TRANSPARENCYG6#$""!!""-%)_VISIBLEG6#""#-%&COLORG6&%$RGBG$""!!""$""!!""$""!!""-%*LINESTYLEG6#""!-%*THICKNESSG6#"""-%-TRANSPARENCYG6#$""!!""-&%&_AXISG6#""#6'-%+_GRIDLINESG6'-%&COLORG6&%$RGBG$""!!""$""!!""$""!!""-%*LINESTYLEG6#""!-%*THICKNESSG6#"""-%-TRANSPARENCYG6#$""!!""-%)_VISIBLEG6#""%-%&COLORG6&%$RGBG$""!!""$""!!""$""!!""-%*LINESTYLEG6#""!-%*THICKNESSG6#"""-%-TRANSPARENCYG6#$""!!""-%+AXESLABELSG6%Q!6"Q!6"-%%FONTG6%%(DEFAULTG%(DEFAULTG"#5-%)_VISIBLEG6#""'-%%ROOTG6'-%)BOUNDS_XG6#$"#q!""-%)BOUNDS_YG6#$"#]!""-%-BOUNDS_WIDTHG6#$"%!)Q!""-%.BOUNDS_HEIGHTG6#$"%!)Q!""-%)CHILDRENG6"-%+ANNOTATIONG6'-%)BOUNDS_XG6#$"#q!""-%)BOUNDS_YG6#$"#]!""-%-BOUNDS_WIDTHG6#$"%!)Q!""-%.BOUNDS_HEIGHTG6#$"%!)Q!""-%)CHILDRENG6*-%/TEXT_CONTAINERG6(-%/LINE_THICKNESSG6#$"#5!""-%(SPATIALG6&-%&TRANSG6#-%'VECTORG6$$""!!""$""!!""-%'ORIGING6#-%&POINTG6$$"2vV)RLnFa;!#9$"2mAdhV"eq^!#:-%&SCALEG6#-%'VECTORG6$$"#5!""$"#5!""-%)ROTATIONG6#$""!!""-%,FIXED_WIDTHG6#%%trueG-%-FIXED_HEIGHTG6#%%trueG-%%DATAG6%7$$"%g:!""$"$S%!""7$$"$]#!""$"$!H!""%'CLOSEDG-%*PARAGRAPHG6#Q_^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"-%/TEXT_CONTAINERG6(-%/LINE_THICKNESSG6#$"#5!""-%(SPATIALG6&-%&TRANSG6#-%'VECTORG6$$""!!""$""!!""-%'ORIGING6#-%&POINTG6$$"1Dc,"z&orM!#8$"1.2AEcB)R#!#8-%&SCALEG6#-%'VECTORG6$$"#5!""$"#5!""-%)ROTATIONG6#$""!!""-%,FIXED_WIDTHG6#%%trueG-%-FIXED_HEIGHTG6#%%trueG-%%DATAG6%7$$"%qK!""$"%5A!""7$$"$]#!""$"$!H!""%'CLOSEDG-%*PARAGRAPHG6#Q_^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"-%/TEXT_CONTAINERG6(-%/LINE_THICKNESSG6#$"#5!""-%(SPATIALG6&-%&TRANSG6#-%'VECTORG6$$""!!""$""!!""-%'ORIGING6#-%&POINTG6$$"1C&os:<V#p!#9$"1)oagq[bJ*!#9-%&SCALEG6#-%'VECTORG6$$"#5!""$"#5!""-%)ROTATIONG6#$""!!""-%,FIXED_WIDTHG6#%%trueG-%-FIXED_HEIGHTG6#%%trueG-%%DATAG6%7$$"#q!""$"$?)!""7$$"%?9!""$"$5$!""%'CLOSEDG-%*PARAGRAPHG6#Q[e[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6"-%/TEXT_CONTAINERG6(-%/LINE_THICKNESSG6#$"#5!""-%(SPATIALG6&-%&TRANSG6#-%'VECTORG6$$""!!""$""!!""-%'ORIGING6#-%&POINTG6$$"1$z7"yGL_l!#9$"2D1*G@=upK!#9-%&SCALEG6#-%'VECTORG6$$"#5!""$"#5!""-%)ROTATIONG6#$""!!""-%,FIXED_WIDTHG6#%%trueG-%-FIXED_HEIGHTG6#%%trueG-%%DATAG6%7$$!#?!""$"%SI!""7$$"%I:!""$"$q#!""%'CLOSEDG-%*PARAGRAPHG6#Qge\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6"-%/TEXT_CONTAINERG6(-%/LINE_THICKNESSG6#$"#5!""-%(SPATIALG6&-%&TRANSG6#-%'VECTORG6$$""!!""$""!!""-%'ORIGING6#-%&POINTG6$$"1G)[]#p"y1$!#8$"2v$4Ys<p*4$!#9-%&SCALEG6#-%'VECTORG6$$"#5!""$"#5!""-%)ROTATIONG6#$""!!""-%,FIXED_WIDTHG6#%%trueG-%-FIXED_HEIGHTG6#%%trueG-%%DATAG6%7$$"%IC!""$"%!)G!""7$$"%q6!""$"$q#!""%'CLOSEDG-%*PARAGRAPHG6#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6"-%/TEXT_CONTAINERG6(-%/LINE_THICKNESSG6#$"#5!""-%(SPATIALG6&-%&TRANSG6#-%'VECTORG6$$""!!""$""!!""-%'ORIGING6#-%&POINTG6$$"1vo/[UgXS!#8$"17.KG!zyV&!#8-%&SCALEG6#-%'VECTORG6$$"#5!""$"#5!""-%)ROTATIONG6#$""!!""-%,FIXED_WIDTHG6#%%trueG-%-FIXED_HEIGHTG6#%%trueG-%%DATAG6%7$$"%5K!""$"%!3&!""7$$"%]9!""$"$q#!""%'CLOSEDG-%*PARAGRAPHG6#Qge\lPFRleHQtZmllbGQgb3BhcXVlPSJmYWxzZSIgc3Vic2NyaXB0PSJmYWxzZSIgdW5kZXJsaW5lPSJmYWxzZSIgc3VwZXJzY3JpcHQ9ImZhbHNlIiBib2xkPSJmYWxzZSIgZm9yZWdyb3VuZD0iWzAsMCwwXSIgaXRhbGljPSJmYWxzZSIgZXhlY3V0YWJsZT0iZmFsc2UiIHNlbGVjdGlvbi1wbGFjZWhvbGRlcj0iZmFsc2UiIHNpemU9IjEyIiByZWFkb25seT0iZmFsc2UiIGJhY2tncm91bmQ9IlsyNTUsMjU1LDI1NV0iIHBsYWNlaG9sZGVyPSJmYWxzZSIgZmFtaWx5PSJUaW1lcyBOZXcgUm9tYW4iIHNwYWNlYWJvdmU9IjAiIGxpbmVicmVhaz0ic3BhY2UiIHJpZ2h0bWFyZ2luPSIwIiBsaW5lc3BhY2luZz0iMC4wIiBpbml0aWFsPSIwIiBmaXJzdGluZGVudD0iMCIgbGVmdG1hcmdpbj0iMCIgYnVsbGV0c3VmZml4PSIiIGFsaWdubWVudD0ibGVmdCIgYnVsbGV0PSJub25lIiBzcGFjZWJlbG93PSIwIiBwYWdlYnJlYWstYmVmb3JlPSJmYWxzZSI+PEVxdWF0aW9uIGV4ZWN1dGFibGU9ImZhbHNlIiBpbnB1dC1lcXVhdGlvbj0iIiBkaXNwbGF5PSJMVWtsYlhKdmQwYzJJeTlKSzIxdlpIVnNaVzVoYldWSE5pSkpMRlI1Y0dWelpYUjBhVzVuUjBrb1gzTjVjMnhwWWtkR0p6WTVMVWtqYlc5SFJpUTJQbEVxSm5WdGFXNTFjekE3UmljdkpTZG1ZVzFwYkhsSFVUQlVhVzFsYzM1T1pYZCtVbTl0WVc1R0p5OGxKWE5wZW1WSFVTTXhORVluTHlVbFltOXNaRWRSSm1aaGJITmxSaWN2SlNkcGRHRnNhV05IUmpjdkpTcDFibVJsY214cGJtVkhSamN2SlNwemRXSnpZM0pwY0hSSFJqY3ZKU3h6ZFhCbGNuTmpjbWx3ZEVkR055OGxLMlp2Y21WbmNtOTFibVJIVVNoYk1Dd3dMREJkUmljdkpTdGlZV05yWjNKdmRXNWtSMUV1V3pJMU5Td3lOVFVzTWpVMVhVWW5MeVVuYjNCaGNYVmxSMFkzTHlVclpYaGxZM1YwWVdKc1pVZEdOeThsS1hKbFlXUnZibXg1UjBZM0x5VXBZMjl0Y0c5elpXUkhSamN2SlNwamIyNTJaWEowWldSSFJqY3ZKU3RwYlhObGJHVmpkR1ZrUjBZM0x5VXNjR3hoWTJWb2IyeGtaWEpIUmpjdkpUWnpaV3hsWTNScGIyNHRjR3hoWTJWb2IyeGtaWEpIUmpjdkpTeHRZWFJvZG1GeWFXRnVkRWRSSjI1dmNtMWhiRVluTHlVbVptVnVZMlZIUmpjdkpTcHpaWEJoY21GMGIzSkhSamN2SlNsemRISmxkR05vZVVkR055OGxLbk41YlcxbGRISnBZMGRHTnk4bEtHeGhjbWRsYjNCSFJqY3ZKUzV0YjNaaFlteGxiR2x0YVhSelIwWTNMeVVuWVdOalpXNTBSMFkzTHlVbmJITndZV05sUjFFc01DNHlNakl5TWpJeVpXMUdKeThsSjNKemNHRmpaVWRHWTI4dFNTTnRhVWRHSkRZMVVTY21JemsyTUR0R0owWXZSakpHTlVZNFJqcEdQRVkrUmtCR1EwWkdSa2hHU2taTVJrNUdVRVpTUmxSR1ZpMUdMRFkrVVNJclJpZEdMMFl5UmpWR09FWTZSanhHUGtaQVJrTkdSa1pJUmtwR1RFWk9SbEJHVWtaVVJsWkdXVVpsYmtabmJrWnBia1piYjBaZGIwWmZiMFpoYjBaa2J5MUdaMjgyTlZFbllYSmpkR0Z1UmlkR0wwWXlSalZHT0VZNlJqeEdQa1pBUmtOR1JrWklSa3BHVEVaT1JsQkdVa1pVUmxZdFNTaHRabVZ1WTJWa1IwWWtOalV0UmlNMk55MUpJMjF1UjBZa05qVlJJakZHSjBZdlJqSkdOVVk0UmpwR1BFWStSa0JHUTBaR1JraEdTa1pNUms1R1VFWlNSbFJHVmkxR0xEWStVU0l2UmlkR0wwWXlSalZHT0VZNlJqeEdQa1pBUmtOR1JrWklSa3BHVEVaT1JsQkdVa1pVUmxaR1dVWmxiaTlHYUc1UkpYUnlkV1ZHSjBacGJrWmJiMFpkYjBaZmJ5OUdZbTlSTERBdU1UWTJOalkyTjJWdFJpY3ZSbVZ2Umw5eExVWm1jRFkxVVNJeVJpZEdMMFl5UmpWR09FWTZSanhHUGtaQVJrTkdSa1pJUmtwR1RFWk9SbEJHVWtaVVJsWkdMeTlHTTFFak1USkdKMFkxUmpoR09rWThSajVHUUVaRFJrWkdTRVpLUmt4R1RrWlFSbEpHVkVaV1JpOUdNa1kxUmpoR09rWThSajVHUUVaRFJrWkdTRVpLUmt4R1RrWlFSbEpHVkVaV1JpOUdaSEZHTlVZNFJqcEdQRVkrUmtCR1EwWkdSa2hHU2taTVJrNUdVRVpTUmxSR1ZnPT0iPkxVa2xiWEp2ZDBjMkl5OUpLMjF2WkhWc1pXNWhiV1ZITmlKSkxGUjVjR1Z6WlhSMGFXNW5SMGtvWDNONWMyeHBZa2RHSnpZNUxVa2piVzlIUmlRMlBsRXFKblZ0YVc1MWN6QTdSaWN2SlNkbVlXMXBiSGxIVVRCVWFXMWxjMzVPWlhkK1VtOXRZVzVHSnk4bEpYTnBlbVZIVVNNeE5FWW5MeVVsWW05c1pFZFJKbVpoYkhObFJpY3ZKU2RwZEdGc2FXTkhSamN2SlNwMWJtUmxjbXhwYm1WSFJqY3ZKU3B6ZFdKelkzSnBjSFJIUmpjdkpTeHpkWEJsY25OamNtbHdkRWRHTnk4bEsyWnZjbVZuY205MWJtUkhVU2hiTUN3d0xEQmRSaWN2SlN0aVlXTnJaM0p2ZFc1a1IxRXVXekkxTlN3eU5UVXNNalUxWFVZbkx5VW5iM0JoY1hWbFIwWTNMeVVyWlhobFkzVjBZV0pzWlVkR055OGxLWEpsWVdSdmJteDVSMFkzTHlVcFkyOXRjRzl6WldSSFJqY3ZKU3BqYjI1MlpYSjBaV1JIUmpjdkpTdHBiWE5sYkdWamRHVmtSMFkzTHlVc2NHeGhZMlZvYjJ4a1pYSkhSamN2SlRaelpXeGxZM1JwYjI0dGNHeGhZMlZvYjJ4a1pYSkhSamN2SlN4dFlYUm9kbUZ5YVdGdWRFZFJKMjV2Y20xaGJFWW5MeVVtWm1WdVkyVkhSamN2SlNwelpYQmhjbUYwYjNKSFJqY3ZKU2x6ZEhKbGRHTm9lVWRHTnk4bEtuTjViVzFsZEhKcFkwZEdOeThsS0d4aGNtZGxiM0JIUmpjdkpTNXRiM1poWW14bGJHbHRhWFJ6UjBZM0x5VW5ZV05qWlc1MFIwWTNMeVVuYkhOd1lXTmxSMUVzTUM0eU1qSXlNakl5WlcxR0p5OGxKM0p6Y0dGalpVZEdZMjh0U1NOdGFVZEdKRFkxVVNjbUl6azJNRHRHSjBZdlJqSkdOVVk0UmpwR1BFWStSa0JHUTBaR1JraEdTa1pNUms1R1VFWlNSbFJHVmkxR0xEWStVU0lyUmlkR0wwWXlSalZHT0VZNlJqeEdQa1pBUmtOR1JrWklSa3BHVEVaT1JsQkdVa1pVUmxaR1dVWmxia1puYmtacGJrWmJiMFpkYjBaZmIwWmhiMFprYnkxR1oyODJOVkVuWVhKamRHRnVSaWRHTDBZeVJqVkdPRVk2Ump4R1BrWkFSa05HUmtaSVJrcEdURVpPUmxCR1VrWlVSbFl0U1NodFptVnVZMlZrUjBZa05qVXRSaU0yTnkxSkkyMXVSMFlrTmpWUklqRkdKMFl2UmpKR05VWTRSanBHUEVZK1JrQkdRMFpHUmtoR1NrWk1SazVHVUVaU1JsUkdWaTFHTERZK1VTSXZSaWRHTDBZeVJqVkdPRVk2Ump4R1BrWkFSa05HUmtaSVJrcEdURVpPUmxCR1VrWlVSbFpHV1VabGJpOUdhRzVSSlhSeWRXVkdKMFpwYmtaYmIwWmRiMFpmYnk5R1ltOVJMREF1TVRZMk5qWTJOMlZ0UmljdlJtVnZSbDl4TFVabWNEWTFVU0l5UmlkR0wwWXlSalZHT0VZNlJqeEdQa1pBUmtOR1JrWklSa3BHVEVaT1JsQkdVa1pVUmxaR0x5OUdNMUVqTVRKR0owWTFSamhHT2tZOFJqNUdRRVpEUmtaR1NFWktSa3hHVGtaUVJsSkdWRVpXUmk5R01rWTFSamhHT2tZOFJqNUdRRVpEUmtaR1NFWktSa3hHVGtaUVJsSkdWRVpXUmk5R1pIRkdOVVk0UmpwR1BFWStSa0JHUTBaR1JraEdTa1pNUms1R1VFWlNSbFJHVmc9PTwvRXF1YXRpb24+PC9UZXh0LWZpZWxkPg==6"-%/TEXT_CONTAINERG6(-%/LINE_THICKNESSG6#$"#5!""-%(SPATIALG6&-%&TRANSG6#-%'VECTORG6$$""!!""$""!!""-%'ORIGING6#-%&POINTG6$$"1c,T&z_DB$!#8$"1c,;*QOK&**!#9-%&SCALEG6#-%'VECTORG6$$"#5!""$"#5!""-%)ROTATIONG6#$""!!""-%,FIXED_WIDTHG6#%%trueG-%-FIXED_HEIGHTG6#%%trueG-%%DATAG6%7$$"%SE!""$"$+*!""7$$"%g5!""$"$q#!""%'CLOSEDG-%*PARAGRAPHG6#Q[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6"-%/TEXT_CONTAINERG6(-%/LINE_THICKNESSG6#$"#5!""-%(SPATIALG6&-%&TRANSG6#-%'VECTORG6$$""!!""$""!!""-%'ORIGING6#-%&POINTG6$$"1p/t[u>qH!#8$"16iO+N&eK"!#8-%&SCALEG6#-%'VECTORG6$$"#5!""$"#5!""-%)ROTATIONG6#$""!!""-%,FIXED_WIDTHG6#%%trueG-%-FIXED_HEIGHTG6#%%trueG-%%DATAG6%7$$");REF!"&$")z#f@"!"&7$$"$I%!""$"$]#!""%'CLOSEDG-%*PARAGRAPHG6#Q[iuPFRleHQtZmllbGQgb3BhcXVlPSJmYWxzZSIgc3Vic2NyaXB0PSJmYWxzZSIgdW5kZXJsaW5lPSJmYWxzZSIgc3VwZXJzY3JpcHQ9ImZhbHNlIiBib2xkPSJmYWxzZSIgZm9yZWdyb3VuZD0iWzAsMCwwXSIgaXRhbGljPSJmYWxzZSIgZXhlY3V0YWJsZT0iZmFsc2UiIHNlbGVjdGlvbi1wbGFjZWhvbGRlcj0iZmFsc2UiIHNpemU9IjEyIiByZWFkb25seT0iZmFsc2UiIGJhY2tncm91bmQ9IlsyNTUsMjU1LDI1NV0iIHBsYWNlaG9sZGVyPSJmYWxzZSIgZmFtaWx5PSJUaW1lcyBOZXcgUm9tYW4iIHNwYWNlYWJvdmU9IjAiIGxpbmVicmVhaz0ic3BhY2UiIHJpZ2h0bWFyZ2luPSIwIiBsaW5lc3BhY2luZz0iMC4wIiBpbml0aWFsPSIwIiBmaXJzdGluZGVudD0iMCIgbGVmdG1hcmdpbj0iMCIgYnVsbGV0c3VmZml4PSIiIGFsaWdubWVudD0ibGVmdCIgYnVsbGV0PSJub25lIiBzcGFjZWJlbG93PSIwIiBwYWdlYnJlYWstYmVmb3JlPSJmYWxzZSI+PEVxdWF0aW9uIGV4ZWN1dGFibGU9ImZhbHNlIiBpbnB1dC1lcXVhdGlvbj0iIiBkaXNwbGF5PSJMVWtsYlhKdmQwYzJJeTlKSzIxdlpIVnNaVzVoYldWSE5pSkpMRlI1Y0dWelpYUjBhVzVuUjBrb1gzTjVjMnhwWWtkR0p6WTNMVWtqYldsSFJpUTJJMUVoUmljdFJpTTJOa1lyTFVrbWJYTnhjblJIUmlRMkpTMUdJelkxTFVramJXNUhSaVEyTlZFaU5VWW5MeVVuWm1GdGFXeDVSMUV3VkdsdFpYTitUbVYzZmxKdmJXRnVSaWN2SlNWemFYcGxSMUVqTVRSR0p5OGxKV0p2YkdSSFVTWm1ZV3h6WlVZbkx5VW5hWFJoYkdsalIwWkNMeVVxZFc1a1pYSnNhVzVsUjBaQ0x5VXFjM1ZpYzJOeWFYQjBSMFpDTHlVc2MzVndaWEp6WTNKcGNIUkhSa0l2SlN0bWIzSmxaM0p2ZFc1a1IxRW9XekFzTUN3d1hVWW5MeVVyWW1GamEyZHliM1Z1WkVkUkxsc3lOVFVzTWpVMUxESTFOVjFHSnk4bEoyOXdZWEYxWlVkR1FpOGxLMlY0WldOMWRHRmliR1ZIUmtJdkpTbHlaV0ZrYjI1c2VVZEdRaThsS1dOdmJYQnZjMlZrUjBaQ0x5VXFZMjl1ZG1WeWRHVmtSMFpDTHlVcmFXMXpaV3hsWTNSbFpFZEdRaThsTEhCc1lXTmxhRzlzWkdWeVIwWkNMeVUyYzJWc1pXTjBhVzl1TFhCc1lXTmxhRzlzWkdWeVIwWkNMeVVzYldGMGFIWmhjbWxoYm5SSFVTZHViM0p0WVd4R0owWTZSajFHUUVaRFJrVkdSMFpKUmt0R1RrWlJSbE5HVlVaWFJsbEdaVzVHWjI1R2FXNUdXMjlHUzBaT1JqcEdQVVpBUmtOR1JVWkhSa2xHUzBaT1JsRkdVMFpWUmxkR1dVWmxia1puYmtacGJrWmJiMFlyUmpvdlJqNVJJekV5UmlkR1FFWkRSa1ZHUjBaSlJrdEdUa1pSUmxOR1ZVWlhSbGxHWlc1R1oyNUdhVzVHVzI4PSI+TFVrbGJYSnZkMGMySXk5SksyMXZaSFZzWlc1aGJXVkhOaUpKTEZSNWNHVnpaWFIwYVc1blIwa29YM041YzJ4cFlrZEdKelkzTFVramJXbEhSaVEySTFFaFJpY3RSaU0yTmtZckxVa21iWE54Y25SSFJpUTJKUzFHSXpZMUxVa2piVzVIUmlRMk5WRWlOVVluTHlVblptRnRhV3g1UjFFd1ZHbHRaWE4rVG1WM2ZsSnZiV0Z1UmljdkpTVnphWHBsUjFFak1UUkdKeThsSldKdmJHUkhVU1ptWVd4elpVWW5MeVVuYVhSaGJHbGpSMFpDTHlVcWRXNWtaWEpzYVc1bFIwWkNMeVVxYzNWaWMyTnlhWEIwUjBaQ0x5VXNjM1Z3WlhKelkzSnBjSFJIUmtJdkpTdG1iM0psWjNKdmRXNWtSMUVvV3pBc01Dd3dYVVluTHlVclltRmphMmR5YjNWdVpFZFJMbHN5TlRVc01qVTFMREkxTlYxR0p5OGxKMjl3WVhGMVpVZEdRaThsSzJWNFpXTjFkR0ZpYkdWSFJrSXZKU2x5WldGa2IyNXNlVWRHUWk4bEtXTnZiWEJ2YzJWa1IwWkNMeVVxWTI5dWRtVnlkR1ZrUjBaQ0x5VXJhVzF6Wld4bFkzUmxaRWRHUWk4bExIQnNZV05sYUc5c1pHVnlSMFpDTHlVMmMyVnNaV04wYVc5dUxYQnNZV05sYUc5c1pHVnlSMFpDTHlVc2JXRjBhSFpoY21saGJuUkhVU2R1YjNKdFlXeEdKMFk2UmoxR1FFWkRSa1ZHUjBaSlJrdEdUa1pSUmxOR1ZVWlhSbGxHWlc1R1oyNUdhVzVHVzI5R1MwWk9SanBHUFVaQVJrTkdSVVpIUmtsR1MwWk9SbEZHVTBaVlJsZEdXVVpsYmtabmJrWnBia1piYjBZclJqb3ZSajVSSXpFeVJpZEdRRVpEUmtWR1IwWkpSa3RHVGtaUlJsTkdWVVpYUmxsR1pXNUdaMjVHYVc1R1cyOD08L0VxdWF0aW9uPjwvVGV4dC1maWVsZD4=6"Ig==A sinusoidal function is any constant linear combination of a cosine and sine of the same frequency LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEnJiM5Njk7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGMS8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYuUSI+RidGMkY0LyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGSy1JI21uR0YkNiVRIjBGJ0YyRjRGMkY0:
sinusoidLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkobWZlbmNlZEdGJDYmLUYjNiYtSSNtaUdGJDYnUSJ4RicvJSVzaXplR1EjMTRGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJ0Y0RjovRj5RJ25vcm1hbEYnRjRGOkZARjRGOkZA = 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.
The second expression is the equivalent phase-shifted cosine form of the sinusoidal function.
We set the frequency to 1 for these diagrams.The amplitude 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 the phase shift LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEnJiM5NDg7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGMS8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRidGMkY0 (satisfying 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 )LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LlEifkYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGRUYvRjI= are polar coordinates in the plane of the Cartesian coordinates 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 parametrizing the sinusoidal functions 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. The unique phase shift 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 is limited to shifting left or right an angle less than 180 degrees.
We give an example of 4 different sinusoidal functions with the same amplitude LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkmbXNxcnRHRiQ2Iy1GIzYlLUkjbW5HRiQ2JVEiNUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRjRGNy1JI21vR0YkNi5RKSZhcHByb3g7RidGNEY3LyUmZmVuY2VHRjYvJSpzZXBhcmF0b3JHRjYvJSlzdHJldGNoeUdGNi8lKnN5bW1ldHJpY0dGNi8lKGxhcmdlb3BHRjYvJS5tb3ZhYmxlbGltaXRzR0Y2LyUnYWNjZW50R0Y2LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTi1GMTYlUSUyLjI0RidGNEY3RjRGNw== and acute reference angle, but in each of the 4 different quadrants of the coefficient plane for this kind of function. The acute reference angle in each case is 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 but we need to pick the polar angle between LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LlEqJnVtaW51czA7RicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0ZFLUkjbWlHRiQ2JlEnJiM5NjA7RicvJSdpdGFsaWNHRjFGL0YyRi9GMg== and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEnJiM5NjA7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGMS8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRidGMkY0.
These are the four corresponding sinusoidal functions for these cases: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 means that 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
[2,1]:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LlEifkYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGRUYrRi9GMg==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
[2,-1]:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LlEifkYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGRUYrRi9GMg==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYsLUkjbW5HRiQ2JVEiMkYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LlEifkYnRi9GMi8lJmZlbmNlR0YxLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRjEvJSpzeW1tZXRyaWNHRjEvJShsYXJnZW9wR0YxLyUubW92YWJsZWxpbWl0c0dGMS8lJ2FjY2VudEdGMS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkktSSNtaUdGJDYmUSRjb3NGJy8lJ2l0YWxpY0dGMUYvRjItSShtZmVuY2VkR0YkNiUtRiM2Ji1GTTYmUSJ4RicvRlFRJXRydWVGJ0YvL0YzUSdpdGFsaWNGJ0YvLyUwZm9udF9zdHlsZV9uYW1lR1EpMkR+SW5wdXRGJ0YyRi9GMi1GNjYuUSomdW1pbnVzMDtGJ0YvRjJGOUY7Rj1GP0ZBRkNGRS9GSFEsMC4yMjIyMjIyZW1GJy9GS0Zfby1GTTYmUSRzaW5GJ0ZQRi9GMi1GUzYlLUYjNiZGV0Y1Ri9GMkYvRjItRjY2LlEiPUYnRi9GMkY5RjtGPUY/RkFGQ0ZFL0ZIUSwwLjI3Nzc3NzhlbUYnL0ZLRlxwRi9GMg==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYsLUkmbXNxcnRHRiQ2Iy1GIzYmLUkjbW5HRiQ2JVEiNUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRjQvJTBmb250X3N0eWxlX25hbWVHUSkyRH5JbnB1dEYnRjctSSNtb0dGJDYuUSJ+RidGNEY3LyUmZmVuY2VHRjYvJSpzZXBhcmF0b3JHRjYvJSlzdHJldGNoeUdGNi8lKnN5bW1ldHJpY0dGNi8lKGxhcmdlb3BHRjYvJS5tb3ZhYmxlbGltaXRzR0Y2LyUnYWNjZW50R0Y2LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGUS1JI21pR0YkNiZRJGNvc0YnLyUnaXRhbGljR0Y2RjRGNy1JKG1mZW5jZWRHRiQ2JS1GIzYpLUZVNiZRInhGJy9GWVEldHJ1ZUYnRjQvRjhRJ2l0YWxpY0YnLUY+Ni5RIitGJ0Y0RjdGQUZDRkVGR0ZJRktGTS9GUFEsMC4yMjIyMjIyZW1GJy9GU0Zkby1GVTYmUSdhcmN0YW5GJ0ZYRjRGNy1GZW42JS1GIzYmLUkmbWZyYWNHRiQ2KC1GMTYlUSIxRidGNEY3LUYjNiYtRjE2JVEiMkYnRjRGN0Y0RjpGNy8lLmxpbmV0aGlja25lc3NHRmJwLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRlxxLyUpYmV2ZWxsZWRHRjZGNEY6RjdGNEY3RjRGOkY3RjRGNy1GVTYjUSFGJy1JJ21zcGFjZUdGJDYmLyUnaGVpZ2h0R1EmMC4wZXhGJy8lJndpZHRoR0ZRLyUmZGVwdGhHRmlxLyUqbGluZWJyZWFrR1EobmV3bGluZUYnRj1GNEY6Rjc=[-2,1]: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[-2,-1]: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Now plot the corresponding sinusoidal functions 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 for one half period before and after LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTi1JI21uR0YkNiVRIjBGJ0YyRjwtSSdtc3BhY2VHRiQ2Ji8lJ2hlaWdodEdRJjAuMGV4RicvJSZ3aWR0aEdRJjAuMGVtRicvJSZkZXB0aEdGWi8lKmxpbmVicmVha0dRKG5ld2xpbmVGJy1GVjYmRlhGZW5GaG4vRltvUSVhdXRvRictRiw2I1EhRidGMkY8 (one full cycle centered at the origin). The lag and lead interpretation is for x as a time variable (see below).
The red curve (1st quadrant) is lagging slightly behind
the black unshifted cosine (peaks at later LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEieEYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dGMS8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSxib2xkLWl0YWxpY0YnLyUrZm9udHdlaWdodEdRJWJvbGRGJ0YvRjQvRjhGPEY6), while
the blue curve (4th quadrant) is slightly leading the black unshifted cosine (peaks at earlier LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn), while
the green (2nd quadrant) and
the cyan (3rd quadrant) curves are lagging behind nearly by a half cycle (or leading by a bit more than a half cycle).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 we show two full cycles: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We can explore all the possibilities with a slider.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
SSZkZWx0YUc2Ig==#
# The following code is autogenerated by the Explore command. Do not edit.
#
Explore:-Runtime:-Update( plot([sqrt(5), -sqrt(5), sqrt(5)*cos(x), sqrt(5)*cos(x-delta)],x = -Pi .. Pi,y = -2.5 .. 2.5,color = [black $ 3, red],gridlines = true), ':-Plot0', [':-delta'], ':-sliders'=["Sliderdelta"], ':-labels'=["Labeldelta"],':-isplot'=true, ':-handlers'=[delta=__nohandler]);
#
# End of autogenerated code.
#
lagging and leading: depends on space or time!Moving wave on spatial coordinate axis: x is a spatial distance variableIf we think of a wave traveling to the right on the x-axis as time progresses, then when the phase shift is positive (blue curve as shown in the animation below) the peaks of the phase-shifted wave arrive at any given position ahead in time of the standard cosine wave, i.e., lead the standard cosine wave (phase-shifted cosine is to the right on the plot). Vice versa, if the phase shift is negative, the phase-shifted cosine wave lags behind the standard cosine wave in the sense that its peaks arrive later than the standard curve (phase-shifted cosine is to the right on the plot).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 oscillation plotted versus time: x is a time variable
On the other hand if we simply compare two sinusoidal functions representing an oscillation in the vertical spatial direction versus time, then a positive phase shift means that the peak occurs later in time (lags behind the standard cosine, to the right on the time line) while a a negative phase shift means that the peak occurs before in time (leads the standard cosine, to the left on the time line) .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Thus "lagging and leading" depends on the interpretation of the context of the sinusoidal function, and is opposite for an oscillation compared to a traveling wave.plot 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