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- Equation:
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Equation 2sinxcos3x+sin4x=0
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Equation x^2-9x+20=0
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Equation cos*((pi(4x+48))/4)=-(sqrt(2)/2)
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Identical expressions
- 2sinxcos3x+sin4x= zero
- 2 sinus of x co sinus of e of 3x plus sinus of 4x equally 0
- 2 sinus of x co sinus of e of 3x plus sinus of 4x equally zero
- 2sinxcos3x+sin4x=O
-
Similar expressions
- 2sinxcos3x-sin4x=0
2sinxcos3x+sin4x=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
2*sin(x)*cos(3*x) + sin(4*x) = 0
$$2 \sin{\left(x \right)} \cos{\left(3 x \right)} + \sin{\left(4 x \right)} = 0$$
Sum and product of roots
[src]
sum
/ ______________ \ / ______________ \
/ / ____\ \ / / ____\ \ | / ____ | | / ____ |
pi pi I*\- log\1 - I*\/ 15 / + log(4)/ I*\- log\1 + I*\/ 15 / + log(4)/ |-\/ 1 - I*\/ 15 | |-\/ 1 + I*\/ 15 |
0 + 0 - -- + -- + pi + -------------------------------- + -------------------------------- - I*log|-------------------| - I*log|-------------------|
2 2 2 2 \ 2 / \ 2 /
$$- i \log{\left(- \frac{\sqrt{1 + \sqrt{15} i}}{2} \right)} - \left(- \pi + i \log{\left(- \frac{\sqrt{1 - \sqrt{15} i}}{2} \right)} - \frac{i \left(\log{\left(4 \right)} - \log{\left(1 + \sqrt{15} i \right)}\right)}{2} - \frac{i \left(\log{\left(4 \right)} - \log{\left(1 - \sqrt{15} i \right)}\right)}{2}\right)$$
=
/ ______________ \ / ______________ \
/ / ____\ \ / / ____\ \ | / ____ | | / ____ |
I*\- log\1 + I*\/ 15 / + log(4)/ I*\- log\1 - I*\/ 15 / + log(4)/ |-\/ 1 + I*\/ 15 | |-\/ 1 - I*\/ 15 |
pi + -------------------------------- + -------------------------------- - I*log|-------------------| - I*log|-------------------|
2 2 \ 2 / \ 2 /
$$- i \log{\left(- \frac{\sqrt{1 + \sqrt{15} i}}{2} \right)} - i \log{\left(- \frac{\sqrt{1 - \sqrt{15} i}}{2} \right)} + \pi + \frac{i \left(\log{\left(4 \right)} - \log{\left(1 - \sqrt{15} i \right)}\right)}{2} + \frac{i \left(\log{\left(4 \right)} - \log{\left(1 + \sqrt{15} i \right)}\right)}{2}$$
product
/ ______________ \ / ______________ \
/ / ____\ \ / / ____\ \ | / ____ | | / ____ |
-pi pi I*\- log\1 - I*\/ 15 / + log(4)/ I*\- log\1 + I*\/ 15 / + log(4)/ |-\/ 1 - I*\/ 15 | |-\/ 1 + I*\/ 15 |
1*0*----*--*pi*--------------------------------*--------------------------------*-I*log|-------------------|*-I*log|-------------------|
2 2 2 2 \ 2 / \ 2 /
$$- i \log{\left(- \frac{\sqrt{1 + \sqrt{15} i}}{2} \right)} - i \log{\left(- \frac{\sqrt{1 - \sqrt{15} i}}{2} \right)} \frac{i \left(\log{\left(4 \right)} - \log{\left(1 + \sqrt{15} i \right)}\right)}{2} \frac{i \left(\log{\left(4 \right)} - \log{\left(1 - \sqrt{15} i \right)}\right)}{2} \pi \frac{\pi}{2} 1 \cdot 0 \left(- \frac{\pi}{2}\right)$$
=
0
$$0$$
0
Rapid solution
[src]
x1 = 0
$$x_{1} = 0$$
-pi
x2 = ----
2
$$x_{2} = - \frac{\pi}{2}$$
pi
x3 = --
2
$$x_{3} = \frac{\pi}{2}$$
x4 = pi
$$x_{4} = \pi$$
/ / ____\ \
I*\- log\1 - I*\/ 15 / + log(4)/
x5 = --------------------------------
2
$$x_{5} = \frac{i \left(\log{\left(4 \right)} - \log{\left(1 - \sqrt{15} i \right)}\right)}{2}$$
/ / ____\ \
I*\- log\1 + I*\/ 15 / + log(4)/
x6 = --------------------------------
2
$$x_{6} = \frac{i \left(\log{\left(4 \right)} - \log{\left(1 + \sqrt{15} i \right)}\right)}{2}$$
/ ______________ \
| / ____ |
|-\/ 1 - I*\/ 15 |
x7 = -I*log|-------------------|
\ 2 /
$$x_{7} = - i \log{\left(- \frac{\sqrt{1 - \sqrt{15} i}}{2} \right)}$$
/ ______________ \
| / ____ |
|-\/ 1 + I*\/ 15 |
x8 = -I*log|-------------------|
\ 2 /
$$x_{8} = - i \log{\left(- \frac{\sqrt{1 + \sqrt{15} i}}{2} \right)}$$
Numerical answer
[src]
x1 = 16.3670213037754
x2 = -33.8984611536613
x3 = 68.455980343149
x4 = 60.3493184540325
x5 = -87.9645943005142
x6 = -1.5707963267949
x7 = -67.5442420521806
x8 = 46.4648317680205
x9 = 98.04843029711
x10 = -27.6152758464817
x11 = 82.340467029161
x12 = -51.8362787842316
x13 = -76.0572817219814
x14 = 47.7829478396733
x15 = -18.1904978857124
x16 = -15.707963267949
x17 = -55.8896097287899
x18 = -37.6991118430775
x19 = 51.8362787842316
x20 = 54.0661331468529
x21 = 99.871906879047
x22 = 84.163943611098
x23 = 94.2477796076938
x24 = -59.6902604182061
x25 = 7.85398163397448
x26 = 29.845130209103
x27 = -69.7740964148019
x28 = 55.8896097287899
x29 = 76.0572817219814
x30 = 20.4203522483337
x31 = -82.340467029161
x32 = -81.6814089933346
x33 = 0.0
x34 = -84.163943611098
x35 = 91.7652449899304
x36 = -45.553093477052
x37 = -40.1816464608409
x38 = 40.1816464608409
x39 = -3.8006506894162
x40 = 77.8807583039184
x41 = 69.7740964148019
x42 = 14.1371669411541
x43 = -65.9734457253857
x44 = -58.1194640914112
x45 = -25.7917992645448
x46 = 72.2566310325652
x47 = 64.4026493985908
x48 = 24.4736831928919
x49 = -5.62412727135318
x50 = 3.8006506894162
x51 = 73.8274273593601
x52 = -80.1106126665397
x53 = -62.1727950359695
x54 = 36.1283155162826
x55 = 21.9911485751286
x56 = 25.7917992645448
x57 = -43.9822971502571
x58 = -7.85398163397448
x59 = -10.0838359965958
x60 = 6.28318530717959
x61 = 62.1727950359695
x62 = 11.9073125785328
x63 = -19.5086139573652
x64 = -47.7829478396733
x65 = 90.4471289182776
x66 = -95.8185759344887
x67 = -11.9073125785328
x68 = -73.8274273593601
x69 = 86.3937979737193
x70 = -77.8807583039184
x71 = 28.2743338823081
x72 = -99.871906879047
x73 = 42.4115008234622
x74 = 33.8984611536613
x75 = -89.5353906273091
x76 = 18.1904978857124
x77 = 65.9734457253857
x78 = -49.6064244216103
x79 = 43.9822971502571
x80 = -41.4997625324937
x81 = 50.2654824574367
x82 = -32.0749845717243
x83 = -98.04843029711
x84 = 2.48253461776338
x85 = -23.5619449019235
x86 = 95.8185759344887
x87 = 58.1194640914112
x88 = -91.7652449899304
x89 = -54.0661331468529
x90 = 87.9645943005142
x91 = 10.0838359965958
x92 = -21.9911485751286
x93 = -29.845130209103
x94 = 38.3581698789039
x95 = -14.1371669411541
x96 = 32.0749845717243
x97 = -64.4026493985908
x98 = 80.1106126665397
x99 = -36.1283155162826
x99 = -36.1283155162826
The graph