Mister Exam
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How to use it?
- Equation:
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Equation 4*sin(45-a)*sin(15+a)*cos(15-a)=cos(45-3*a)
-
Equation (x-8)+(x-19)-71x=6
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Equation cos(z)=3
- Equation (x+1)/(x-3)-(8)/(x+3)=24/(x^2-9)
- Express {x} in terms of y where:
- 8*x-7*y=-13
- 9*x+18*y=6
- 15*x-15*y=16
- (x^2+y^2-1)^3+x^2*y^3=0
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Identical expressions
- four *sin(forty-five -a)*sin(fifteen +a)*cos(fifteen -a)=cos(forty-five - three *a)
- 4 multiply by sinus of (45 minus a) multiply by sinus of (15 plus a) multiply by co sinus of e of (15 minus a) equally co sinus of e of (45 minus 3 multiply by a)
- four multiply by sinus of (forty minus five minus a) multiply by sinus of (fifteen plus a) multiply by co sinus of e of (fifteen minus a) equally co sinus of e of (forty minus five minus three multiply by a)
- 4sin(45-a)sin(15+a)cos(15-a)=cos(45-3a)
- 4sin45-asin15+acos15-a=cos45-3a
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Similar expressions
- 4*sin(45-a)*sin(15+a)*cos(15-a)=cos(45+3*a)
- 4*sin(45-a)*sin(15-a)*cos(15-a)=cos(45-3*a)
- 4*sin(45-a)*sin(15+a)*cos(15+a)=cos(45-3*a)
- 4*sin(45+a)*sin(15+a)*cos(15-a)=cos(45-3*a)
4*sin(45-a)*sin(15+a)*cos(15-a)=cos(45-3*a) equation
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The solution
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4*sin(45 - a)*sin(15 + a)*cos(15 - a) = cos(45 - 3*a)
$$4 \sin{\left(45 - a \right)} \sin{\left(a + 15 \right)} \cos{\left(15 - a \right)} = \cos{\left(45 - 3 a \right)}$$
Rapid solution
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/ 15*I\ a1 = -I*log\-I*e /
$$a_{1} = - i \log{\left(- i e^{15 i} \right)}$$
/ 15*I\ a2 = -I*log\I*e /
$$a_{2} = - i \log{\left(i e^{15 i} \right)}$$
Sum and product of roots
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sum
/ 15*I\ / 15*I\ 0 - I*log\-I*e / - I*log\I*e /
$$- i \log{\left(i e^{15 i} \right)} + \left(0 - i \log{\left(- i e^{15 i} \right)}\right)$$
=
/ 15*I\ / 15*I\ - I*log\I*e / - I*log\-I*e /
$$- i \log{\left(i e^{15 i} \right)} - i \log{\left(- i e^{15 i} \right)}$$
product
/ 15*I\ / 15*I\ 1*-I*log\-I*e /*-I*log\I*e /
$$- i \log{\left(i e^{15 i} \right)} 1 \left(- i \log{\left(- i e^{15 i} \right)}\right)$$
=
/ 15*I\ / 15*I\ -log\I*e /*log\-I*e /
$$- \log{\left(- i e^{15 i} \right)} \log{\left(i e^{15 i} \right)}$$
-log(i*exp(15*i))*log(-i*exp(15*i))
Numerical answer
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a1 = 76.261056745001
a2 = 63.6946861306418
a3 = 10.2876110196153
a4 = 7.14601836602552
a5 = -33.6946861306418
a6 = 101.393797973719
a7 = 57.4115008234622
a8 = 66.8362787842316
a9 = -71.3937979737193
a10 = 563.207918051419
a11 = 32.2787595947439
a12 = -5.42035224833366
a13 = 38.5619449019234
a14 = 13.4292036732051
a15 = -39.9778714378214
a16 = -96.5265392024377
a17 = -1271.48219164502
a18 = -43.1194640914112
a19 = -80.8185759344887
a20 = -46.261056745001
a21 = -77.6769832808989
a22 = -58.8274273593601
a23 = -21.1283155162826
a24 = -74.5353906273091
a25 = 98.2522053201295
a26 = 73.1194640914112
a27 = 54.2699081698724
a28 = -52.5442420521806
a29 = 0.86283305884593
a30 = 82.5442420521806
a31 = 47.9867228626928
a32 = 51.1283155162826
a33 = 35.4203522483337
a34 = -65.1106126665397
a35 = 29.1371669411541
a36 = -11.7035375555132
a37 = 4.00442571243572
a38 = 44.845130209103
a39 = -90.2433538952581
a40 = -93.3849465488479
a41 = -68.2522053201295
a42 = 25.9955742875643
a43 = 95.1106126665397
a44 = 91.9690200129499
a45 = 88.8274273593601
a46 = -49.4026493985908
a47 = -27.4115008234622
a48 = -24.2699081698724
a49 = -61.9690200129499
a50 = 19.7123889803847
a51 = -8.56194490192345
a52 = 16.5707963267949
a53 = 107.676983280899
a54 = -36.8362787842316
a55 = -55.6858347057703
a56 = 60.553093477052
a57 = 41.7035375555132
a58 = -14.845130209103
a59 = -30.553093477052
a60 = 85.6858347057703
a61 = -2.27875959474386
a62 = -17.9867228626928
a63 = -99.6681318560275
a64 = -83.9601685880785
a65 = 69.9778714378214
a66 = 79.4026493985908
a67 = -87.1017612416683
a68 = 22.8539816339745
a68 = 22.8539816339745
The graph