Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 9x−9(x+1)=−2x
-
Equation -25-x=-17
-
Equation -x^2+5*x-6=0
- Equation x-y=7
- Express {x} in terms of y where:
- 10*x-15*y=16
- 10*x-18*y=3
- 19*x-12*y=16
- 13*x-12*y=19
- Derivative of:
-
sin(3*x+pi/4)
-
Identical expressions
- sin(three *x+pi/ four)=(-sqrt(three))/ two
- sinus of (3 multiply by x plus Pi divide by 4) equally ( minus square root of (3)) divide by 2
- sinus of (three multiply by x plus Pi divide by four) equally ( minus square root of (three)) divide by two
- sin(3*x+pi/4)=(-√(3))/2
- sin(3x+pi/4)=(-sqrt(3))/2
- sin3x+pi/4=-sqrt3/2
- sin(3*x+pi divide by 4)=(-sqrt(3)) divide by 2
-
Similar expressions
- sin((pi-3*x)/4)=-(sqrt(3)/2)
- cos(x+(2pi/3))=-(sqrt(3)/2)
- sin(3*x+pi/4)=(sqrt(3))/2
- sin(x)*cos(x)=(-sqrt(3))/((2*sin(x)))
- sin(3*x-pi/4)=(-sqrt(3))/2
- sin((pi*(8*x+3)/6))=-sqrt(3)/2
sin(3*x+pi/4)=(-sqrt(3))/2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
___ / pi\ -\/ 3 sin|3*x + --| = ------- \ 4 / 2
$$\sin{\left(3 x + \frac{\pi}{4} \right)} = \frac{\left(-1\right) \sqrt{3}}{2}$$
Detail solution
Given the equation
$$\sin{\left(3 x + \frac{\pi}{4} \right)} = \frac{\left(-1\right) \sqrt{3}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$3 x + \frac{\pi}{4} = 2 \pi n + \operatorname{asin}{\left(- \frac{\sqrt{3}}{2} \right)}$$
$$3 x + \frac{\pi}{4} = 2 \pi n - \operatorname{asin}{\left(- \frac{\sqrt{3}}{2} \right)} + \pi$$
Or
$$3 x + \frac{\pi}{4} = 2 \pi n - \frac{\pi}{3}$$
$$3 x + \frac{\pi}{4} = 2 \pi n + \frac{4 \pi}{3}$$
, where n - is a integer
Move
$$\frac{\pi}{4}$$
to right part of the equation
with the opposite sign, in total:
$$3 x = 2 \pi n - \frac{7 \pi}{12}$$
$$3 x = 2 \pi n + \frac{13 \pi}{12}$$
Divide both parts of the equation by
$$3$$
we get the answer:
$$x_{1} = \frac{2 \pi n}{3} - \frac{7 \pi}{36}$$
$$x_{2} = \frac{2 \pi n}{3} + \frac{13 \pi}{36}$$
$$\sin{\left(3 x + \frac{\pi}{4} \right)} = \frac{\left(-1\right) \sqrt{3}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$3 x + \frac{\pi}{4} = 2 \pi n + \operatorname{asin}{\left(- \frac{\sqrt{3}}{2} \right)}$$
$$3 x + \frac{\pi}{4} = 2 \pi n - \operatorname{asin}{\left(- \frac{\sqrt{3}}{2} \right)} + \pi$$
Or
$$3 x + \frac{\pi}{4} = 2 \pi n - \frac{\pi}{3}$$
$$3 x + \frac{\pi}{4} = 2 \pi n + \frac{4 \pi}{3}$$
, where n - is a integer
Move
$$\frac{\pi}{4}$$
to right part of the equation
with the opposite sign, in total:
$$3 x = 2 \pi n - \frac{7 \pi}{12}$$
$$3 x = 2 \pi n + \frac{13 \pi}{12}$$
Divide both parts of the equation by
$$3$$
we get the answer:
$$x_{1} = \frac{2 \pi n}{3} - \frac{7 \pi}{36}$$
$$x_{2} = \frac{2 \pi n}{3} + \frac{13 \pi}{36}$$
Rapid solution
[src]
-7*pi
x1 = -----
36
$$x_{1} = - \frac{7 \pi}{36}$$
13*pi
x2 = -----
36
$$x_{2} = \frac{13 \pi}{36}$$
x2 = 13*pi/36
Sum and product of roots
[src]
sum
7*pi 13*pi - ---- + ----- 36 36
$$- \frac{7 \pi}{36} + \frac{13 \pi}{36}$$
=
pi -- 6
$$\frac{\pi}{6}$$
product
-7*pi 13*pi -----*----- 36 36
$$- \frac{7 \pi}{36} \frac{13 \pi}{36}$$
=
2 -91*pi ------- 1296
$$- \frac{91 \pi^{2}}{1296}$$
-91*pi^2/1296
Numerical answer
[src]
x1 = 97.8257045742822
x2 = 68.1551072903786
x3 = -19.8094870101356
x4 = 16.1442955809475
x5 = 7.76671517137477
x6 = 95.731309471889
x7 = -11.4319066005629
x8 = -99.3965009010771
x9 = -23.998277214922
x10 = 60.1265927312047
x11 = -76.0090889243531
x12 = -55.41420375082
x13 = 93.6369143694958
x14 = -71.8202987195667
x15 = -78.1034840267462
x16 = -13.5263017029561
x17 = 5.67232006898157
x18 = 80.7214779047377
x19 = 19.9840199353351
x20 = -65.8861792627859
x21 = 72.343897495165
x22 = -67.9805743651791
x23 = 32.5503905496942
x24 = -29.9323966717028
x25 = -17.7150919077424
x26 = -84.3866693339258
x27 = -50.8763476956347
x28 = 91.5425192671026
x29 = -80.1978791291394
x30 = 76.5326876999514
x31 = 24.1728101401215
x32 = -34.1211868764891
x33 = 13219.2110210677
x34 = -61.6973890579996
x35 = -63.7917841603927
x36 = -15.6206968053492
x37 = -59.6029939556064
x38 = 99.9200996766754
x39 = 39.1826417072727
x40 = -38.3099770812755
x41 = 58.0321976288115
x42 = -40.4043721836687
x43 = 22.0784150377283
x44 = 11.9555053761612
x45 = -73.9146938219599
x46 = -88.9245253891111
x47 = 49.6546172192387
x48 = 28.3616003449079
x49 = 89.0990583143105
x50 = 18.2386906833407
x51 = 34.6447856520874
x52 = -44.942228238854
x53 = 51.7490123216319
x54 = 74.4382925975582
x55 = -94.8586448458918
x56 = 36.7391807544806
x57 = 78.6270828023445
x58 = -2.70526034059121
x59 = 47.5602221168455
x60 = 53.8434074240251
x61 = -86.481064436319
x62 = 4052.04365789264
x63 = -36.2155819788823
x64 = -25.7436064669164
x65 = 45.1167611640534
x66 = 14.0499004785544
x67 = -53.3198086484268
x68 = 55.9378025264183
x69 = -69.7259036171735
x70 = -9.33751149816966
x71 = -82.2922742315326
x72 = 70.2495023927718
x73 = 64.315382935991
x74 = -27.8380015693096
x75 = 9.86111027376796
x76 = -21.9038821125288
x77 = 30.4559954473011
x78 = 26.2672052425147
x79 = -3.05432619099008
x80 = -42.4987672860619
x81 = 62.2209878335978
x82 = -49.1310184436404
x83 = 3.57792496658838
x84 = 83.1649388575298
x85 = -57.5085988532132
x86 = -97.3021057986839
x87 = -32.0267917740959
x88 = 43.0223660616602
x89 = 66.0607121879854
x90 = 998.415598603356
x91 = -95.2077106962907
x92 = -7.24311639577647
x93 = 64211.0995131844
x93 = 64211.0995131844