simple solve
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From: adel tekari on 22 Mar 2010 07:54 Dear Matlab users I'm trying to solve the following equation: t=(0:pi/30:2*pi); A=solve('4*sin(t)=tan(pi/30)*6*cos(t)-tan(pi/30)*4/3','t'); I just need the numerical (explicit) values of A. I want to see the t=0.1218 and t=-2.9506 Thanks
From: Walter Roberson on 22 Mar 2010 11:22 adel tekari wrote: > I'm trying to solve the following equation: > > t=(0:pi/30:2*pi); > A=solve('4*sin(t)=tan(pi/30)*6*cos(t)-tan(pi/30)*4/3','t'); > > I just need the numerical (explicit) values of A. I want to see the > t=0.1218 and t=-2.9506 You won't be able to. t=-2.9506 is outside the range 0 to 2*pi that you assign on the first line. The second value will be -2.9506 + 2*pi . I don't know about Matlab's current symbolic engine (MuPad), but Maple solves it fairly directly. Just skip the assignment to t. Maple>> solve(4*sin(t)=tan(Pi/30)*6*cos(t)-tan(Pi/30)*4/3); arctan((-8/3*sin(1/30*Pi)^2*cos(1/30*Pi) - 16/3*sin(1/30*Pi)^3*cos(1/30*Pi) + 1/3*(36*sin(1/30*Pi)^2*cos(1/30*Pi) + 72*sin(1/30*Pi)^3*cos(1/30*Pi)) * (6010/464881 + 46080/464881*sin(1/30*Pi)^3 + 99968/464881*sin(1/30*Pi)^2 - 44480/464881*sin(1/30*Pi) + 2/1394643*(456652987231 - 246369098880*sin(1/30*Pi)^3 - 486622810000*sin(1/30*Pi)^2 + 218499799000*sin(1/30*Pi) + 4777574400*sin(1/30*Pi)^6 + 20729364480*sin(1/30*Pi)^5 + 13262229504*sin(1/30*Pi)^4)^(1/2))) / (6010/464881 + 46080/464881*sin(1/30*Pi)^3 + 99968/464881*sin(1/30*Pi)^2 - 44480/464881*sin(1/30*Pi) + 2/1394643*(456652987231 - 246369098880*sin(1/30*Pi)^3 - 486622810000*sin(1/30*Pi)^2 + 218499799000*sin(1/30*Pi) + 4777574400*sin(1/30*Pi)^6 + 20729364480*sin(1/30*Pi)^5 + 13262229504*sin(1/30*Pi)^4)^(1/2))), arctan((-8/3*sin(1/30*Pi)^2*cos(1/30*Pi) - 16/3*sin(1/30*Pi)^3*cos(1/30*Pi) + 1/3*(36*sin(1/30*Pi)^2*cos(1/30*Pi) + 72*sin(1/30*Pi)^3*cos(1/30*Pi)) * (6010/464881 + 46080/464881*sin(1/30*Pi)^3 + 99968/464881*sin(1/30*Pi)^2 - 44480/464881*sin(1/30*Pi) - 2/1394643*(456652987231 - 246369098880*sin(1/30*Pi)^3 - 486622810000*sin(1/30*Pi)^2 + 218499799000*sin(1/30*Pi) + 4777574400*sin(1/30*Pi)^6 + 20729364480*sin(1/30*Pi)^5 + 13262229504*sin(1/30*Pi)^4)^(1/2))) / (6010/464881 + 46080/464881*sin(1/30*Pi)^3 + 99968/464881*sin(1/30*Pi)^2 - 44480/464881*sin(1/30*Pi) - 2/1394643*(456652987231 - 246369098880*sin(1/30*Pi)^3 - 486622810000*sin(1/30*Pi)^2 + 218499799000*sin(1/30*Pi) + 4777574400*sin(1/30*Pi)^6 + 20729364480*sin(1/30*Pi)^5 + 13262229504*sin(1/30*Pi)^4)^(1/2))) - Pi
From: adel tekari on 22 Mar 2010 11:44 Hi Thank you for your answer. > You won't be able to. t=-2.9506 is outside the range 0 to 2*pi that you > assign on the first line. The second value will be -2.9506 + 2*pi . Actually, what I'm trying to do is to determine the intersction between an ellipse (x=6cos(t), y=4sin(t)) and a line y=mx+p (m=tan(angle), p=yc-tan(angle)*xc; angle=pi/30 , xc=4/3 and yc=0). > I don't know about Matlab's current symbolic engine (MuPad), but Maple > solves it fairly directly. Just skip the assignment to t. > > Maple>> solve(4*sin(t)=tan(Pi/30)*6*cos(t)-tan(Pi/30)*4/3); > > arctan((-8/3*sin(1/30*Pi)^2*cos(1/30*Pi) - > 16/3*sin(1/30*Pi)^3*cos(1/30*Pi) + 1/3*(36*sin(1/30*Pi)^2*cos(1/30*Pi) + > 72*sin(1/30*Pi)^3*cos(1/30*Pi)) * (6010/464881 + > 46080/464881*sin(1/30*Pi)^3 + 99968/464881*sin(1/30*Pi)^2 - > 44480/464881*sin(1/30*Pi) + 2/1394643*(456652987231 - > 246369098880*sin(1/30*Pi)^3 - 486622810000*sin(1/30*Pi)^2 + > 218499799000*sin(1/30*Pi) + 4777574400*sin(1/30*Pi)^6 + > 20729364480*sin(1/30*Pi)^5 + 13262229504*sin(1/30*Pi)^4)^(1/2))) / > (6010/464881 + 46080/464881*sin(1/30*Pi)^3 + 99968/464881*sin(1/30*Pi)^2 > - 44480/464881*sin(1/30*Pi) + 2/1394643*(456652987231 - > 246369098880*sin(1/30*Pi)^3 - 486622810000*sin(1/30*Pi)^2 + > 218499799000*sin(1/30*Pi) + 4777574400*sin(1/30*Pi)^6 + > 20729364480*sin(1/30*Pi)^5 + 13262229504*sin(1/30*Pi)^4)^(1/2))), > > arctan((-8/3*sin(1/30*Pi)^2*cos(1/30*Pi) - > 16/3*sin(1/30*Pi)^3*cos(1/30*Pi) + 1/3*(36*sin(1/30*Pi)^2*cos(1/30*Pi) + > 72*sin(1/30*Pi)^3*cos(1/30*Pi)) * (6010/464881 + > 46080/464881*sin(1/30*Pi)^3 + 99968/464881*sin(1/30*Pi)^2 - > 44480/464881*sin(1/30*Pi) - 2/1394643*(456652987231 - > 246369098880*sin(1/30*Pi)^3 - 486622810000*sin(1/30*Pi)^2 + > 218499799000*sin(1/30*Pi) + 4777574400*sin(1/30*Pi)^6 + > 20729364480*sin(1/30*Pi)^5 + 13262229504*sin(1/30*Pi)^4)^(1/2))) / > (6010/464881 + 46080/464881*sin(1/30*Pi)^3 + 99968/464881*sin(1/30*Pi)^2 > - 44480/464881*sin(1/30*Pi) - 2/1394643*(456652987231 - > 246369098880*sin(1/30*Pi)^3 - 486622810000*sin(1/30*Pi)^2 + > 218499799000*sin(1/30*Pi) + 4777574400*sin(1/30*Pi)^6 + > 20729364480*sin(1/30*Pi)^5 + 13262229504*sin(1/30*Pi)^4)^(1/2))) - Pi With Matlab, I'm able to get the same thing. But I want the values and not the numeric equations ! atan((192320/1394643*sin(1/30*pi)^3*cos(1/30*pi)-130752/464881*sin(1/30*pi)*cos(1/30*pi)-3200/1394643*cos(1/30*pi)-4000/1394643*cos(1/30*pi)^3+1/1394643*(36986982400*sin(1/30*pi)^6*cos(1/30*pi)^2-150877347840*sin(1/30*pi)^4*cos(1/30*pi)^2-1230848000*sin(1/30*pi)^3*cos(1/30*pi)^2-1538560000*sin(1/30*pi)^3*cos(1/30*pi)^4+153864769536*sin(1/30*pi)^2*cos(1/30*pi)^2+2510438400*sin(1/30*pi)*cos(1/30*pi)^2+3138048000*sin(1/30*pi)*cos(1/30*pi)^4+10240000*cos(1/30*pi)^2+25600000*cos(1/30*pi)^4+16000000*cos(1/30*pi)^6+824736084480*sin(1/30*pi)^3+107566490185-796099414880*sin(1/30*pi)+1789219116608*sin(1/30*pi)^2)^(1/2))/(2/9+(16/3*cos(1/30*pi)-32/3*sin(1/30*pi)^3*cos(1/30*pi)-16/3*sin(1/30*pi)^2*cos(1/30*pi)+32/3*sin(1/30*pi)*cos(1/30*pi))*(192320/1394643*sin(1/30*pi)^3*cos(1/30*pi)-130752/464881*sin(1/30*pi)*cos(1/30*pi)-3200/1394643*cos(1/30*pi)-4000/1394643*cos(1/30*pi)^3+1/1394643*(36986982400 *sin(1/30*pi)^6*cos(1/30*pi)^2-150877347840*sin(1/30*pi)^4*cos(1/30*pi)^2-1230848000*sin(1/30*pi)^3*cos(1/30*pi)^2-1538560000*sin(1/30*pi)^3*cos(1/30*pi)^4+153864769536*sin(1/30*pi)^2*cos(1/30*pi)^2+2510438400*sin(1/30*pi)*cos(1/30*pi)^2+3138048000*sin(1/30*pi)*cos(1/30*pi)^4+10240000*cos(1/30*pi)^2+25600000*cos(1/30*pi)^4+16000000*cos(1/30*pi)^6+824736084480*sin(1/30*pi)^3+107566490185-796099414880*sin(1/30*pi)+1789219116608*sin(1/30*pi)^2)^(1/2)))) atan((192320/1394643*sin(1/30*pi)^3*cos(1/30*pi)-130752/464881*sin(1/30*pi)*cos(1/30*pi)-3200/1394643*cos(1/30*pi)-4000/1394643*cos(1/30*pi)^3-1/1394643*(36986982400*sin(1/30*pi)^6*cos(1/30*pi)^2-150877347840*sin(1/30*pi)^4*cos(1/30*pi)^2-1230848000*sin(1/30*pi)^3*cos(1/30*pi)^2-1538560000*sin(1/30*pi)^3*cos(1/30*pi)^4+153864769536*sin(1/30*pi)^2*cos(1/30*pi)^2+2510438400*sin(1/30*pi)*cos(1/30*pi)^2+3138048000*sin(1/30*pi)*cos(1/30*pi)^4+10240000*cos(1/30*pi)^2+25600000*cos(1/30*pi)^4+16000000*cos(1/30*pi)^6+824736084480*sin(1/30*pi)^3+107566490185-796099414880*sin(1/30*pi)+1789219116608*sin(1/30*pi)^2)^(1/2))/(2/9+(16/3*cos(1/30*pi)-32/3*sin(1/30*pi)^3*cos(1/30*pi)-16/3*sin(1/30*pi)^2*cos(1/30*pi)+32/3*sin(1/30*pi)*cos(1/30*pi))*(192320/1394643*sin(1/30*pi)^3*cos(1/30*pi)-130752/464881*sin(1/30*pi)*cos(1/30*pi)-3200/1394643*cos(1/30*pi)-4000/1394643*cos(1/30*pi)^3-1/1394643*(36986982400 *sin(1/30*pi)^6*cos(1/30*pi)^2-150877347840*sin(1/30*pi)^4*cos(1/30*pi)^2-1230848000*sin(1/30*pi)^3*cos(1/30*pi)^2-1538560000*sin(1/30*pi)^3*cos(1/30*pi)^4+153864769536*sin(1/30*pi)^2*cos(1/30*pi)^2+2510438400*sin(1/30*pi)*cos(1/30*pi)^2+3138048000*sin(1/30*pi)*cos(1/30*pi)^4+10240000*cos(1/30*pi)^2+25600000*cos(1/30*pi)^4+16000000*cos(1/30*pi)^6+824736084480*sin(1/30*pi)^3+107566490185-796099414880*sin(1/30*pi)+1789219116608*sin(1/30*pi)^2)^(1/2))))-pi Any help?
From: Matt Fig on 22 Mar 2010 11:48 For numeric values, you could also use FZERO. f = @(t) 4*sin(t)-tan(pi/30)*6*cos(t)+tan(pi/30)*4/3; fzero(f,.1218) % See the help for FZERO.
From: Walter Roberson on 22 Mar 2010 12:06 adel tekari wrote: > With Matlab, I'm able to get the same thing. But I want the values and > not the numeric equations ! > atan((192320/1394643*sin(1/30*pi)^3*cos(1/30*pi)-130752/464881*sin(1/30*pi)*cos(1/30*pi)-3200/1394643*cos(1/30*pi)-4000/1394643*cos(1/30*pi)^3+1/1394643*(36986982400*sin(1/30*pi)^6*cos(1/30*pi)^2-150877347840*sin(1/30*pi)^4*cos(1/30*pi)^2-1230848000*sin(1/30*pi)^3*cos(1/30*pi)^2-1538560000*sin(1/30*pi)^3*cos(1/30*pi)^4+153864769536*sin(1/30*pi)^2*cos(1/30*pi)^2+2510438400*sin(1/30*pi)*cos(1/30*pi)^2+3138048000*sin(1/30*pi)*cos(1/30*pi)^4+10240000*cos(1/30*pi)^2+25600000*cos(1/30*pi)^4+16000000*cos(1/30*pi)^6+824736084480*sin(1/30*pi)^3+107566490185-796099414880*sin(1/30*pi)+1789219116608*sin(1/30*pi)^2)^(1/2))/(2/9+(16/3*cos(1/30*pi)-32/3*sin(1/30*pi)^3*cos(1/30*pi)-16/3*sin(1/30*pi)^2*cos(1/30*pi)+32/3*sin(1/30*pi)*cos(1/30*pi))*(192320/1394643*sin(1/30*pi)^3*cos(1/30*pi)-130752/464881*sin(1/30*pi)*cos(1/30*pi)-3200/1394643*cos(1/30*pi)-4000/1394643*cos(1/30*pi)^3+1/1394643*(36986982400 > *sin(1/30*pi)^6*cos(1/30*pi)^2-150877347840*sin(1/30*pi)^4*cos(1/30*pi)^2-1230848000*sin(1/30*pi)^3*cos(1/30*pi)^2-1538560000*sin(1/30*pi)^3*cos(1/30*pi)^4+153864769536*sin(1/30*pi)^2*cos(1/30*pi)^2+2510438400*sin(1/30*pi)*cos(1/30*pi)^2+3138048000*sin(1/30*pi)*cos(1/30*pi)^4+10240000*cos(1/30*pi)^2+25600000*cos(1/30*pi)^4+16000000*cos(1/30*pi)^6+824736084480*sin(1/30*pi)^3+107566490185-796099414880*sin(1/30*pi)+1789219116608*sin(1/30*pi)^2)^(1/2)))) > > atan((192320/1394643*sin(1/30*pi)^3*cos(1/30*pi)-130752/464881*sin(1/30*pi)*cos(1/30*pi)-3200/1394643*cos(1/30*pi)-4000/1394643*cos(1/30*pi)^3-1/1394643*(36986982400*sin(1/30*pi)^6*cos(1/30*pi)^2-150877347840*sin(1/30*pi)^4*cos(1/30*pi)^2-1230848000*sin(1/30*pi)^3*cos(1/30*pi)^2-1538560000*sin(1/30*pi)^3*cos(1/30*pi)^4+153864769536*sin(1/30*pi)^2*cos(1/30*pi)^2+2510438400*sin(1/30*pi)*cos(1/30*pi)^2+3138048000*sin(1/30*pi)*cos(1/30*pi)^4+10240000*cos(1/30*pi)^2+25600000*cos(1/30*pi)^4+16000000*cos(1/30*pi)^6+824736084480*sin(1/30*pi)^3+107566490185-796099414880*sin(1/30*pi)+1789219116608*sin(1/30*pi)^2)^(1/2))/(2/9+(16/3*cos(1/30*pi)-32/3*sin(1/30*pi)^3*cos(1/30*pi)-16/3*sin(1/30*pi)^2*cos(1/30*pi)+32/3*sin(1/30*pi)*cos(1/30*pi))*(192320/1394643*sin(1/30*pi)^3*cos(1/30*pi)-130752/464881*sin(1/30*pi)*cos(1/30*pi)-3200/1394643*cos(1/30*pi)-4000/1394643*cos(1/30*pi)^3-1/1394643*(36986982400 > *sin(1/30*pi)^6*cos(1/30*pi)^2-150877347840*sin(1/30*pi)^4*cos(1/30*pi)^2-1230848000*sin(1/30*pi)^3*cos(1/30*pi)^2-1538560000*sin(1/30*pi)^3*cos(1/30*pi)^4+153864769536*sin(1/30*pi)^2*cos(1/30*pi)^2+2510438400*sin(1/30*pi)*cos(1/30*pi)^2+3138048000*sin(1/30*pi)*cos(1/30*pi)^4+10240000*cos(1/30*pi)^2+25600000*cos(1/30*pi)^4+16000000*cos(1/30*pi)^6+824736084480*sin(1/30*pi)^3+107566490185-796099414880*sin(1/30*pi)+1789219116608*sin(1/30*pi)^2)^(1/2))))-pi Call double() passing in the symbolic expression to be evaluated.
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