Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation x/9+x=-10/3
-
Equation z^4+1=0
-
Equation (x-5)^2=(x+10)^2
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Equation -3x-9=2x
- Express {x} in terms of y where:
- 18*x-8*y=-2
- 4*x+2*y=5
- 1*x+10*y=-18
- 18*x-11*y=2
- Sum of series:
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0.5
- Integral of d{x}:
- 0.5
- 0.5
-
Identical expressions
- sin^4x+cos^4x+cos2x= zero . five
- sinus of to the power of 4x plus co sinus of e of to the power of 4x plus co sinus of e of 2x equally 0.5
- sinus of to the power of 4x plus co sinus of e of to the power of 4x plus co sinus of e of 2x equally zero . five
- sin4x+cos4x+cos2x=0.5
- sin⁴x+cos⁴x+cos2x=0.5
- sin^4x+cos^4x+cos2x=O.5
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Similar expressions
- sin^4x-cos^4x+cos2x=0.5
- (Abs(2*log(0.)*5*(x)-3))=-log(0.)*5*(x)
- sin^4x+cos^4x-cos2x=0.5
sin^4x+cos^4x+cos2x=0.5 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
4 4 sin (x) + cos (x) + cos(2*x) = 1/2
$$\left(\sin^{4}{\left(x \right)} + \cos^{4}{\left(x \right)}\right) + \cos{\left(2 x \right)} = \frac{1}{2}$$
Rapid solution
[src]
-3*pi
x1 = -----
4
$$x_{1} = - \frac{3 \pi}{4}$$
-pi
x2 = ----
4
$$x_{2} = - \frac{\pi}{4}$$
pi
x3 = --
4
$$x_{3} = \frac{\pi}{4}$$
3*pi
x4 = ----
4
$$x_{4} = \frac{3 \pi}{4}$$
/ ___\
pi I*log\2 - \/ 3 /
x5 = - -- - ----------------
2 2
$$x_{5} = - \frac{\pi}{2} - \frac{i \log{\left(2 - \sqrt{3} \right)}}{2}$$
/ ___\
pi I*log\2 + \/ 3 /
x6 = - -- - ----------------
2 2
$$x_{6} = - \frac{\pi}{2} - \frac{i \log{\left(\sqrt{3} + 2 \right)}}{2}$$
/ ___\
pi I*log\2 - \/ 3 /
x7 = -- - ----------------
2 2
$$x_{7} = \frac{\pi}{2} - \frac{i \log{\left(2 - \sqrt{3} \right)}}{2}$$
/ ___\
pi I*log\2 + \/ 3 /
x8 = -- - ----------------
2 2
$$x_{8} = \frac{\pi}{2} - \frac{i \log{\left(\sqrt{3} + 2 \right)}}{2}$$
x8 = pi/2 - i*log(sqrt(3) + 2)/2
Sum and product of roots
[src]
sum
/ ___\ / ___\ / ___\ / ___\ 3*pi pi pi 3*pi pi I*log\2 - \/ 3 / pi I*log\2 + \/ 3 / pi I*log\2 - \/ 3 / pi I*log\2 + \/ 3 / - ---- - -- + -- + ---- + - -- - ---------------- + - -- - ---------------- + -- - ---------------- + -- - ---------------- 4 4 4 4 2 2 2 2 2 2 2 2
$$\left(\frac{\pi}{2} - \frac{i \log{\left(\sqrt{3} + 2 \right)}}{2}\right) + \left(\left(\left(- \frac{\pi}{2} - \frac{i \log{\left(\sqrt{3} + 2 \right)}}{2}\right) + \left(\left(\left(\left(- \frac{3 \pi}{4} - \frac{\pi}{4}\right) + \frac{\pi}{4}\right) + \frac{3 \pi}{4}\right) + \left(- \frac{\pi}{2} - \frac{i \log{\left(2 - \sqrt{3} \right)}}{2}\right)\right)\right) + \left(\frac{\pi}{2} - \frac{i \log{\left(2 - \sqrt{3} \right)}}{2}\right)\right)$$
=
/ ___\ / ___\ - I*log\2 + \/ 3 / - I*log\2 - \/ 3 /
$$- i \log{\left(\sqrt{3} + 2 \right)} - i \log{\left(2 - \sqrt{3} \right)}$$
product
/ / ___\\ / / ___\\ / / ___\\ / / ___\\ -3*pi -pi pi 3*pi | pi I*log\2 - \/ 3 /| | pi I*log\2 + \/ 3 /| |pi I*log\2 - \/ 3 /| |pi I*log\2 + \/ 3 /| -----*----*--*----*|- -- - ----------------|*|- -- - ----------------|*|-- - ----------------|*|-- - ----------------| 4 4 4 4 \ 2 2 / \ 2 2 / \2 2 / \2 2 /
$$\frac{3 \pi}{4} \frac{\pi}{4} \cdot - \frac{3 \pi}{4} \left(- \frac{\pi}{4}\right) \left(- \frac{\pi}{2} - \frac{i \log{\left(2 - \sqrt{3} \right)}}{2}\right) \left(- \frac{\pi}{2} - \frac{i \log{\left(\sqrt{3} + 2 \right)}}{2}\right) \left(\frac{\pi}{2} - \frac{i \log{\left(2 - \sqrt{3} \right)}}{2}\right) \left(\frac{\pi}{2} - \frac{i \log{\left(\sqrt{3} + 2 \right)}}{2}\right)$$
=
4 / / ___\\ / / ___\\ / / ___\\ / / ___\\
9*pi *\pi + I*log\2 + \/ 3 //*\pi + I*log\2 - \/ 3 //*\pi - I*log\2 + \/ 3 //*\pi - I*log\2 - \/ 3 //
-----------------------------------------------------------------------------------------------------
4096
$$\frac{9 \pi^{4} \left(\pi - i \log{\left(2 - \sqrt{3} \right)}\right) \left(\pi + i \log{\left(2 - \sqrt{3} \right)}\right) \left(\pi - i \log{\left(\sqrt{3} + 2 \right)}\right) \left(\pi + i \log{\left(\sqrt{3} + 2 \right)}\right)}{4096}$$
9*pi^4*(pi + i*log(2 + sqrt(3)))*(pi + i*log(2 - sqrt(3)))*(pi - i*log(2 + sqrt(3)))*(pi - i*log(2 - sqrt(3)))/4096
Numerical answer
[src]
x1 = 25.9181393921158
x2 = -99.7455667514759
x3 = 74.6128255227576
x4 = -54.1924732744239
x5 = 22.776546738526
x6 = -90.3207887907066
x7 = 18.0641577581413
x8 = 82.4668071567321
x9 = 38.484510006475
x10 = 46.3384916404494
x11 = -77.7544181763474
x12 = -76.1836218495525
x13 = -5.49778714378214
x14 = -38.484510006475
x15 = 76.1836218495525
x16 = 54.1924732744239
x17 = 55.7632696012188
x18 = 27.4889357189107
x19 = 5.49778714378214
x20 = 2.35619449019234
x21 = 84.037603483527
x22 = 33.7721210260903
x23 = -62.0464549083984
x24 = 91.8915851175014
x25 = -85.6083998103219
x26 = -33.7721210260903
x27 = 10.2101761241668
x28 = -2110.36486504894
x29 = -30.6305283725005
x30 = -19.6349540849362
x31 = -69.9004365423729
x32 = -32.2013246992954
x33 = 88.7499924639117
x34 = -40.0553063332699
x35 = -10.2101761241668
x36 = -82.4668071567321
x37 = -101.316363078271
x38 = -60.4756585816035
x39 = 98.174770424681
x40 = 49.4800842940392
x41 = 11.7809724509617
x42 = 90.3207887907066
x43 = -25.9181393921158
x44 = 68.329640215578
x45 = 16.4933614313464
x46 = 3.92699081698724
x47 = -98.174770424681
x48 = -41.6261026600648
x49 = -47.9092879672443
x50 = -93.4623814442964
x51 = 520.718982332508
x52 = -296.095107600838
x53 = -55.7632696012188
x54 = 24.3473430653209
x55 = -27.4889357189107
x56 = -91.8915851175014
x57 = -84.037603483527
x58 = 40.0553063332699
x59 = 44.7676953136546
x60 = -850.586210959436
x61 = -11.7809724509617
x62 = -463374.70622837
x63 = -15612.9300901779
x64 = -63.6172512351933
x65 = 896.139304436488
x66 = -71.4712328691678
x67 = -3.92699081698724
x68 = 32.2013246992954
x69 = -49.4800842940392
x70 = -16.4933614313464
x71 = 77.7544181763474
x72 = 60.4756585816035
x73 = 47.9092879672443
x74 = 69.9004365423729
x75 = -68.329640215578
x76 = 62.0464549083984
x77 = 99.7455667514759
x78 = 66.7588438887831
x79 = -18.0641577581413
x79 = -18.0641577581413