Mister Exam
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How to use it?
- Equation:
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Equation 13/(x+6)=2
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Equation x^2=18
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Equation -3(x-1)=24-10x
- Equation 7*x^3-63*x=0
- Express {x} in terms of y where:
- 14*x+5*y=11
- -17*x-12*y=-4
- 8*x-7*y=-1
- 20*x-5*y=-7
- Derivative of:
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cos(4x)
- Integral of d{x}:
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cos(4x)
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Identical expressions
- sin(7x)-sin(x)=cos(4x)
- sinus of (7x) minus sinus of (x) equally co sinus of e of (4x)
- sin7x-sinx=cos4x
-
Similar expressions
- cos(4*x)=-1
- sin(7*x)-sin(x)=0
- sin(7x)+sin(x)=cos(4x)
- sin(x)^(8)+cos(x)^(8)=1/32*(cos(x)^(24)+14*cos(4*x)+17)
- 2cos2xcos7x-cos4x=1
- sin(7x)-sinx=cos(4x)
sin(7x)-sin(x)=cos(4x) equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
sin(7*x) - sin(x) = cos(4*x)
$$- \sin{\left(x \right)} + \sin{\left(7 x \right)} = \cos{\left(4 x \right)}$$
Rapid solution
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-7*pi
x1 = -----
8
$$x_{1} = - \frac{7 \pi}{8}$$
-3*pi
x2 = -----
8
$$x_{2} = - \frac{3 \pi}{8}$$
pi
x3 = --
8
$$x_{3} = \frac{\pi}{8}$$
5*pi
x4 = ----
8
$$x_{4} = \frac{5 \pi}{8}$$
/ ___________ ___________\
| / ___ / ___ |
/log(8) / ___\\ |\/ 2 + \/ 2 + \/ 2 - \/ 2 |
x5 = I*|------ - log\2*\/ 2 /| + atan|-------------------------------|
\ 2 / | ___________ ___________|
| / ___ / ___ |
\\/ 2 + \/ 2 - \/ 2 - \/ 2 /
$$x_{5} = \operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}}{- \sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}} \right)} + i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right)$$
/ ___________ ___________\
| / ___ / ___ |
/log(8) / ___\\ |\/ 2 - \/ 2 - \/ 2 + \/ 2 |
x6 = I*|------ - log\2*\/ 2 /| + atan|-------------------------------|
\ 2 / | ___________ ___________|
| / ___ / ___ |
\\/ 2 + \/ 2 + \/ 2 - \/ 2 /
$$x_{6} = \operatorname{atan}{\left(\frac{- \sqrt{\sqrt{2} + 2} + \sqrt{2 - \sqrt{2}}}{\sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}} \right)} + i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right)$$
/ ___________ ___________ \
| / ___ / ___ |
/log(8) / ___\\ | \/ 2 + \/ 2 - \/ 2 - \/ 2 |
x7 = pi + I*|------ - log\2*\/ 2 /| + atan|---------------------------------|
\ 2 / | ___________ ___________|
| / ___ / ___ |
\- \/ 2 + \/ 2 - \/ 2 - \/ 2 /
$$x_{7} = \operatorname{atan}{\left(\frac{- \sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}}{- \sqrt{\sqrt{2} + 2} - \sqrt{2 - \sqrt{2}}} \right)} + \pi + i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right)$$
/ / ___________ ___________\ \
| | / ___ / ___ | |
|-\- \/ 2 + \/ 2 - \/ 2 - \/ 2 / | /log(8) / ___\\
x8 = -pi - atan|-------------------------------------| + I*|------ - log\2*\/ 2 /|
| ___________ ___________ | \ 2 /
| / ___ / ___ |
\ \/ 2 - \/ 2 - \/ 2 + \/ 2 /
$$x_{8} = - \pi - \operatorname{atan}{\left(- \frac{- \sqrt{\sqrt{2} + 2} - \sqrt{2 - \sqrt{2}}}{- \sqrt{\sqrt{2} + 2} + \sqrt{2 - \sqrt{2}}} \right)} + i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right)$$
x8 = -pi - atan(-(-sqrt(sqrt(2) + 2) - sqrt(2 - sqrt(2)))/(-sqrt(sqrt(2) + 2) + sqrt(2 - sqrt(2)))) + i*(-log(2*sqrt(2)) + log(8)/2)
Sum and product of roots
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sum
/ ___________ ___________\ / ___________ ___________\ / ___________ ___________ \ / / ___________ ___________\ \
| / ___ / ___ | | / ___ / ___ | | / ___ / ___ | | | / ___ / ___ | |
7*pi 3*pi pi 5*pi /log(8) / ___\\ |\/ 2 + \/ 2 + \/ 2 - \/ 2 | /log(8) / ___\\ |\/ 2 - \/ 2 - \/ 2 + \/ 2 | /log(8) / ___\\ | \/ 2 + \/ 2 - \/ 2 - \/ 2 | |-\- \/ 2 + \/ 2 - \/ 2 - \/ 2 / | /log(8) / ___\\
- ---- - ---- + -- + ---- + I*|------ - log\2*\/ 2 /| + atan|-------------------------------| + I*|------ - log\2*\/ 2 /| + atan|-------------------------------| + pi + I*|------ - log\2*\/ 2 /| + atan|---------------------------------| + -pi - atan|-------------------------------------| + I*|------ - log\2*\/ 2 /|
8 8 8 8 \ 2 / | ___________ ___________| \ 2 / | ___________ ___________| \ 2 / | ___________ ___________| | ___________ ___________ | \ 2 /
| / ___ / ___ | | / ___ / ___ | | / ___ / ___ | | / ___ / ___ |
\\/ 2 + \/ 2 - \/ 2 - \/ 2 / \\/ 2 + \/ 2 + \/ 2 - \/ 2 / \- \/ 2 + \/ 2 - \/ 2 - \/ 2 / \ \/ 2 - \/ 2 - \/ 2 + \/ 2 /
$$\left(\left(\left(\left(\left(\left(- \frac{7 \pi}{8} - \frac{3 \pi}{8}\right) + \frac{\pi}{8}\right) + \frac{5 \pi}{8}\right) + \left(\operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}}{- \sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}} \right)} + i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right)\right)\right) + \left(\operatorname{atan}{\left(\frac{- \sqrt{\sqrt{2} + 2} + \sqrt{2 - \sqrt{2}}}{\sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}} \right)} + i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right)\right)\right) + \left(\operatorname{atan}{\left(\frac{- \sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}}{- \sqrt{\sqrt{2} + 2} - \sqrt{2 - \sqrt{2}}} \right)} + \pi + i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right)\right)\right) + \left(- \pi - \operatorname{atan}{\left(- \frac{- \sqrt{\sqrt{2} + 2} - \sqrt{2 - \sqrt{2}}}{- \sqrt{\sqrt{2} + 2} + \sqrt{2 - \sqrt{2}}} \right)} + i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right)\right)$$
=
/ / ___________ ___________\ \ / ___________ ___________\ / ___________ ___________\ / ___________ ___________ \
| | / ___ / ___ | | | / ___ / ___ | | / ___ / ___ | | / ___ / ___ |
|-\- \/ 2 + \/ 2 - \/ 2 - \/ 2 / | pi /log(8) / ___\\ |\/ 2 - \/ 2 - \/ 2 + \/ 2 | |\/ 2 + \/ 2 + \/ 2 - \/ 2 | | \/ 2 + \/ 2 - \/ 2 - \/ 2 |
- atan|-------------------------------------| - -- + 4*I*|------ - log\2*\/ 2 /| + atan|-------------------------------| + atan|-------------------------------| + atan|---------------------------------|
| ___________ ___________ | 2 \ 2 / | ___________ ___________| | ___________ ___________| | ___________ ___________|
| / ___ / ___ | | / ___ / ___ | | / ___ / ___ | | / ___ / ___ |
\ \/ 2 - \/ 2 - \/ 2 + \/ 2 / \\/ 2 + \/ 2 + \/ 2 - \/ 2 / \\/ 2 + \/ 2 - \/ 2 - \/ 2 / \- \/ 2 + \/ 2 - \/ 2 - \/ 2 /
$$- \frac{\pi}{2} + \operatorname{atan}{\left(\frac{- \sqrt{\sqrt{2} + 2} + \sqrt{2 - \sqrt{2}}}{\sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}} \right)} + \operatorname{atan}{\left(\frac{- \sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}}{- \sqrt{\sqrt{2} + 2} - \sqrt{2 - \sqrt{2}}} \right)} - \operatorname{atan}{\left(- \frac{- \sqrt{\sqrt{2} + 2} - \sqrt{2 - \sqrt{2}}}{- \sqrt{\sqrt{2} + 2} + \sqrt{2 - \sqrt{2}}} \right)} + \operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}}{- \sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}} \right)} + 4 i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right)$$
product
/ / ___________ ___________\\ / / ___________ ___________\\ / / ___________ ___________ \\ / / / ___________ ___________\ \ \
| | / ___ / ___ || | | / ___ / ___ || | | / ___ / ___ || | | | / ___ / ___ | | |
-7*pi -3*pi pi 5*pi | /log(8) / ___\\ |\/ 2 + \/ 2 + \/ 2 - \/ 2 || | /log(8) / ___\\ |\/ 2 - \/ 2 - \/ 2 + \/ 2 || | /log(8) / ___\\ | \/ 2 + \/ 2 - \/ 2 - \/ 2 || | |-\- \/ 2 + \/ 2 - \/ 2 - \/ 2 / | /log(8) / ___\\|
-----*-----*--*----*|I*|------ - log\2*\/ 2 /| + atan|-------------------------------||*|I*|------ - log\2*\/ 2 /| + atan|-------------------------------||*|pi + I*|------ - log\2*\/ 2 /| + atan|---------------------------------||*|-pi - atan|-------------------------------------| + I*|------ - log\2*\/ 2 /||
8 8 8 8 | \ 2 / | ___________ ___________|| | \ 2 / | ___________ ___________|| | \ 2 / | ___________ ___________|| | | ___________ ___________ | \ 2 /|
| | / ___ / ___ || | | / ___ / ___ || | | / ___ / ___ || | | / ___ / ___ | |
\ \\/ 2 + \/ 2 - \/ 2 - \/ 2 // \ \\/ 2 + \/ 2 + \/ 2 - \/ 2 // \ \- \/ 2 + \/ 2 - \/ 2 - \/ 2 // \ \ \/ 2 - \/ 2 - \/ 2 + \/ 2 / /
$$\frac{5 \pi}{8} \frac{\pi}{8} \cdot - \frac{7 \pi}{8} \left(- \frac{3 \pi}{8}\right) \left(\operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}}{- \sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}} \right)} + i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right)\right) \left(\operatorname{atan}{\left(\frac{- \sqrt{\sqrt{2} + 2} + \sqrt{2 - \sqrt{2}}}{\sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}} \right)} + i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right)\right) \left(\operatorname{atan}{\left(\frac{- \sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}}{- \sqrt{\sqrt{2} + 2} - \sqrt{2 - \sqrt{2}}} \right)} + \pi + i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right)\right) \left(- \pi - \operatorname{atan}{\left(- \frac{- \sqrt{\sqrt{2} + 2} - \sqrt{2 - \sqrt{2}}}{- \sqrt{\sqrt{2} + 2} + \sqrt{2 - \sqrt{2}}} \right)} + i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right)\right)$$
=
/ / ___________ ___________\\ / / ___________ ___________\\ / ___________ ___________\ / ___________ ___________\
| | / ___ / ___ || | | / ___ / ___ || | / ___ / ___ | | / ___ / ___ |
4 | |\/ 2 - \/ 2 - \/ 2 + \/ 2 || | |\/ 2 + \/ 2 + \/ 2 - \/ 2 || |\/ 2 - \/ 2 - \/ 2 + \/ 2 | |\/ 2 + \/ 2 + \/ 2 - \/ 2 |
105*pi *|pi + atan|-------------------------------||*|pi + atan|-------------------------------||*atan|-------------------------------|*atan|-------------------------------|
| | ___________ ___________|| | | ___________ ___________|| | ___________ ___________| | ___________ ___________|
| | / ___ / ___ || | | / ___ / ___ || | / ___ / ___ | | / ___ / ___ |
\ \\/ 2 + \/ 2 + \/ 2 - \/ 2 // \ \\/ 2 - \/ 2 - \/ 2 + \/ 2 // \\/ 2 + \/ 2 + \/ 2 - \/ 2 / \\/ 2 - \/ 2 - \/ 2 + \/ 2 /
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4096
$$\frac{105 \pi^{4} \left(\operatorname{atan}{\left(\frac{- \sqrt{\sqrt{2} + 2} + \sqrt{2 - \sqrt{2}}}{\sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}} \right)} + \pi\right) \left(\operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}}{- \sqrt{\sqrt{2} + 2} + \sqrt{2 - \sqrt{2}}} \right)} + \pi\right) \operatorname{atan}{\left(\frac{- \sqrt{\sqrt{2} + 2} + \sqrt{2 - \sqrt{2}}}{\sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}} \right)} \operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}}{- \sqrt{\sqrt{2} + 2} + \sqrt{2 - \sqrt{2}}} \right)}}{4096}$$
105*pi^4*(pi + atan((sqrt(2 - sqrt(2)) - sqrt(2 + sqrt(2)))/(sqrt(2 + sqrt(2)) + sqrt(2 - sqrt(2)))))*(pi + atan((sqrt(2 + sqrt(2)) + sqrt(2 - sqrt(2)))/(sqrt(2 - sqrt(2)) - sqrt(2 + sqrt(2)))))*atan((sqrt(2 - sqrt(2)) - sqrt(2 + sqrt(2)))/(sqrt(2 + sqrt(2)) + sqrt(2 - sqrt(2))))*atan((sqrt(2 + sqrt(2)) + sqrt(2 - sqrt(2)))/(sqrt(2 - sqrt(2)) - sqrt(2 + sqrt(2))))/4096
Numerical answer
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x1 = 83.9503370209273
x2 = -98.2620368872808
x3 = 67.9369411338793
x4 = 52.2289778659303
x5 = -13.7444678594553
x6 = 82.0741080750334
x7 = -57.7703982410123
x8 = -64.009950316892
x9 = -87.7900613753148
x10 = -22.165681500328
x11 = -20.0276531666349
x12 = 53.0143760293278
x13 = -49.872783375738
x14 = 39.9680398706701
x15 = -66.3661448070844
x16 = 23.9546439836222
x17 = 60.0829594999048
x18 = -91.9788515801012
x19 = -9.8174770424681
x20 = 96.2112750161874
x21 = 72.0820981073658
x22 = 69.9877030049726
x23 = 4.31968989868597
x24 = 42.0188017417635
x25 = 56.1559686829176
x26 = -67.9369411338793
x27 = -8.24668071567321
x28 = -78.7143492649443
x29 = 32.2885911618951
x30 = 74.2201264410589
x31 = 12.1736715326604
x32 = -79.717913584841
x33 = 92.2842841992002
x34 = 46.2512251778497
x35 = -78.9325154214436
x36 = 90.2335223281068
x37 = -4.01425727958696
x38 = -5.89048622548086
x39 = 102.799892942466
x40 = 48.3019870489431
x41 = -1.96349540849362
x42 = 71.8639319508665
x43 = -17.9768912955416
x44 = 0.174532925199433
x45 = 65.5807466436869
x46 = -35.7356164345839
x47 = -86.0010988920206
x48 = 64.009950316892
x49 = -34.9502182711865
x50 = -82.0741080750334
x51 = 30.2378292908018
x52 = 96.5167076352864
x53 = -47.9965544298441
x54 = -75.0055246044563
x55 = -27.8816348006094
x56 = -93.8550805259951
x57 = -88.3572933822129
x58 = -55.3705705195201
x59 = 8.24668071567321
x60 = -97.7820713429823
x61 = -31.2413936106985
x62 = 38.0918109247762
x63 = 10.6465084371654
x64 = 2.26892802759263
x65 = -23.9546439836222
x66 = -75.7909227678538
x67 = 41.233403578366
x68 = -31.8086256175967
x69 = -15.8824961931484
x70 = 9.03207887907065
x71 = -11.693705988362
x72 = -53.7997741927252
x73 = -61.9591884457987
x74 = 16.1006623496477
x75 = -39.6626072515711
x76 = 44.1568300754565
x77 = 34.164820107789
x78 = -96.9966731795849
x79 = 14.5298660228528
x80 = -83.6449044018282
x81 = -42.0188017417635
x82 = 88.1391272257137
x83 = 86.0010988920206
x84 = 20.0276531666349
x85 = 64.7953484802895
x86 = -71.8639319508665
x87 = 28.0998009571087
x88 = -98.5674695063798
x89 = 26.0054058547155
x90 = 29.4524311274043
x91 = 76.2708883121522
x92 = -43.8077642250577
x93 = -59.8647933434055
x94 = 100.138265833175
x95 = 78.1471172580461
x95 = 78.1471172580461