Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation (2x-4)(x-11)+28=0
- Equation 3x^2-28x+9=0
- Equation 5-8cos^2x=sin2x
- Equation x=(4*a^4+1*a^4-104)/4
- Express {x} in terms of y where:
- -1*x-19*y=-10
- 5*x+5*y=20
- 4*x-16*y=6
- sqrt(x^2+y^2+4x-6y-12)+(x^2+10x-27)=8-|y-9|+|y-3|
- Graphing y =:
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sin2x
- Derivative of:
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sin2x
- Sum of series:
- sin2x
-
Identical expressions
- five -8cos^2x=sin2x
- 5 minus 8 co sinus of e of squared x equally sinus of 2x
- five minus 8 co sinus of e of squared x equally sinus of 2x
- 5-8cos2x=sin2x
- 5-8cos²x=sin2x
- 5-8cos to the power of 2x=sin2x
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Similar expressions
- 5sin^2*x-12sinx+4=0
- 2cos^3x-2cosx-sin^2x=0
- 5+8cos^2x=sin2x
5-8cos^2x=sin2x equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
2 5 - 8*cos (x) = sin(2*x)
$$5 - 8 \cos^{2}{\left(x \right)} = \sin{\left(2 x \right)}$$
Sum and product of roots
[src]
sum
pi /log(34) / ____\\ /log(34) / ____\\ / ___\ -- + pi - atan(3/5) + I*|------- - log\\/ 34 /| + -atan(3/5) + I*|------- - log\\/ 34 /| - I*log\-\/ I / 4 \ 2 / \ 2 /
$$- i \log{\left(- \sqrt{i} \right)} + \left(\left(\frac{\pi}{4} + \left(- \operatorname{atan}{\left(\frac{3}{5} \right)} + \pi + i \left(- \log{\left(\sqrt{34} \right)} + \frac{\log{\left(34 \right)}}{2}\right)\right)\right) + \left(- \operatorname{atan}{\left(\frac{3}{5} \right)} + i \left(- \log{\left(\sqrt{34} \right)} + \frac{\log{\left(34 \right)}}{2}\right)\right)\right)$$
=
5*pi / ___\ /log(34) / ____\\
-2*atan(3/5) + ---- - I*log\-\/ I / + 2*I*|------- - log\\/ 34 /|
4 \ 2 /
$$- i \log{\left(- \sqrt{i} \right)} - 2 \operatorname{atan}{\left(\frac{3}{5} \right)} + \frac{5 \pi}{4} + 2 i \left(- \log{\left(\sqrt{34} \right)} + \frac{\log{\left(34 \right)}}{2}\right)$$
product
pi / /log(34) / ____\\\ / /log(34) / ____\\\ / / ___\\ --*|pi - atan(3/5) + I*|------- - log\\/ 34 /||*|-atan(3/5) + I*|------- - log\\/ 34 /||*\-I*log\-\/ I // 4 \ \ 2 // \ \ 2 //
$$- i \log{\left(- \sqrt{i} \right)} \frac{\pi}{4} \left(- \operatorname{atan}{\left(\frac{3}{5} \right)} + \pi + i \left(- \log{\left(\sqrt{34} \right)} + \frac{\log{\left(34 \right)}}{2}\right)\right) \left(- \operatorname{atan}{\left(\frac{3}{5} \right)} + i \left(- \log{\left(\sqrt{34} \right)} + \frac{\log{\left(34 \right)}}{2}\right)\right)$$
=
/ ___\
pi*I*(pi - atan(3/5))*atan(3/5)*log\-\/ I /
-------------------------------------------
4
$$\frac{i \pi \left(\pi - \operatorname{atan}{\left(\frac{3}{5} \right)}\right) \log{\left(- \sqrt{i} \right)} \operatorname{atan}{\left(\frac{3}{5} \right)}}{4}$$
pi*i*(pi - atan(3/5))*atan(3/5)*log(-sqrt(i))/4
Rapid solution
[src]
pi
x1 = --
4
$$x_{1} = \frac{\pi}{4}$$
/log(34) / ____\\
x2 = pi - atan(3/5) + I*|------- - log\\/ 34 /|
\ 2 /
$$x_{2} = - \operatorname{atan}{\left(\frac{3}{5} \right)} + \pi + i \left(- \log{\left(\sqrt{34} \right)} + \frac{\log{\left(34 \right)}}{2}\right)$$
/log(34) / ____\\
x3 = -atan(3/5) + I*|------- - log\\/ 34 /|
\ 2 /
$$x_{3} = - \operatorname{atan}{\left(\frac{3}{5} \right)} + i \left(- \log{\left(\sqrt{34} \right)} + \frac{\log{\left(34 \right)}}{2}\right)$$
/ ___\ x4 = -I*log\-\/ I /
$$x_{4} = - i \log{\left(- \sqrt{i} \right)}$$
x4 = -i*log(-sqrt(i))
Numerical answer
[src]
x1 = 71.7162115322947
x2 = 25.9181393921158
x3 = -99.7455667514759
x4 = 18.3091364212682
x5 = 68.5746188787049
x6 = -96.6039740978861
x7 = -90.3207887907066
x8 = 90.5657674538334
x9 = -38.2395313433481
x10 = -60.2306799184767
x11 = 82.4668071567321
x12 = 38.484510006475
x13 = -298.991721591301
x14 = -77.7544181763474
x15 = -69.655457879246
x16 = 5.742765806909
x17 = -5.49778714378214
x18 = 76.1836218495525
x19 = -16.2483827682195
x20 = 54.1924732744239
x21 = -82.2218284936052
x22 = -3.68201215386038
x23 = -62.0464549083984
x24 = 91.8915851175014
x25 = 63.6172512351933
x26 = 85.6083998103219
x27 = -33.7721210260903
x28 = 10.2101761241668
x29 = 2.60117315331921
x30 = 24.5923217284478
x31 = 49.7250629571661
x32 = -19.3899754218093
x33 = 40.3002849963967
x34 = -47.6643093041175
x35 = -75.9386431864256
x36 = -40.0553063332699
x37 = -97.9297917615542
x38 = 93.7073601074232
x39 = 84.2825821466538
x40 = 98.174770424681
x41 = -85.363421147195
x42 = 34.0170996892171
x43 = -57.0890872648869
x44 = 121519.405014007
x45 = -24.3473430653209
x46 = 16.4933614313464
x47 = 3.92699081698724
x48 = 74.8578041858844
x49 = -46.3384916404494
x50 = 12.0259511140886
x51 = -93.4623814442964
x52 = -2.35619449019234
x53 = 41.6261026600648
x54 = -55.7632696012188
x55 = -27.4889357189107
x56 = -84.037603483527
x57 = -11.7809724509617
x58 = 77.9993968394742
x59 = 99.9905454146028
x60 = -63.3722725720664
x61 = 62.2914335715253
x62 = 56.0082482643457
x63 = -71.4712328691678
x64 = -31.9563460361685
x65 = 32.2013246992954
x66 = -49.4800842940392
x67 = 46.5834703035763
x68 = -91.6466064543746
x69 = -41.3811239969379
x70 = 60.4756585816035
x71 = 27.7339143820376
x72 = 47.9092879672443
x73 = 69.9004365423729
x74 = -25.6731607289889
x75 = -68.329640215578
x76 = -9.96519746103996
x77 = 19.6349540849362
x78 = 131.406471950501
x79 = -18.0641577581413
x80 = -53.9474946112971
x81 = -50.8059019577073
x81 = -50.8059019577073