Mister Exam
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- Equation:
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Equation x^4=81
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Equation 12/(x-15)=15/(x-12)
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Equation ||x|-4|=5
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Equation 3^x=1
- Express {x} in terms of y where:
- -14*x+19*y=-3
- -12*x-13*y=-2
- -3*x-1*y=-9
- -4*x-12*y=13
-
Identical expressions
- sin(6x+пи)=-√ two / two
- sinus of (6x plus пи) equally minus √2 divide by 2
- sinus of (6x plus пи) equally minus √ two divide by two
- sin6x+пи=-√2/2
- sin(6x+пи)=-√2 divide by 2
-
Similar expressions
- (4x^4-(√2/2)x^2+1)(4x^4+(√2/2)x^2+1)=0
- sin(6x-пи)=-√2/2
- sin(6x+пи)=+√2/2
sin(6x+пи)=-√2/2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
___
-\/ 2
sin(6*x + pi) = -------
2
$$\sin{\left(6 x + \pi \right)} = \frac{\left(-1\right) \sqrt{2}}{2}$$
Detail solution
Given the equation
$$\sin{\left(6 x + \pi \right)} = \frac{\left(-1\right) \sqrt{2}}{2}$$
- this is the simplest trigonometric equation
The equation is transformed to
$$\sin{\left(6 x \right)} = \frac{\sqrt{2}}{2}$$
This equation is transformed to
$$6 x = 2 \pi n + \operatorname{asin}{\left(\frac{\sqrt{2}}{2} \right)}$$
$$6 x = 2 \pi n - \operatorname{asin}{\left(\frac{\sqrt{2}}{2} \right)} + \pi$$
Or
$$6 x = 2 \pi n + \frac{\pi}{4}$$
$$6 x = 2 \pi n + \frac{3 \pi}{4}$$
, where n - is a integer
Divide both parts of the equation by
$$6$$
we get the answer:
$$x_{1} = \frac{\pi n}{3} + \frac{\pi}{24}$$
$$x_{2} = \frac{\pi n}{3} + \frac{\pi}{8}$$
$$\sin{\left(6 x + \pi \right)} = \frac{\left(-1\right) \sqrt{2}}{2}$$
- this is the simplest trigonometric equation
Divide both parts of the equation by -1
The equation is transformed to
$$\sin{\left(6 x \right)} = \frac{\sqrt{2}}{2}$$
This equation is transformed to
$$6 x = 2 \pi n + \operatorname{asin}{\left(\frac{\sqrt{2}}{2} \right)}$$
$$6 x = 2 \pi n - \operatorname{asin}{\left(\frac{\sqrt{2}}{2} \right)} + \pi$$
Or
$$6 x = 2 \pi n + \frac{\pi}{4}$$
$$6 x = 2 \pi n + \frac{3 \pi}{4}$$
, where n - is a integer
Divide both parts of the equation by
$$6$$
we get the answer:
$$x_{1} = \frac{\pi n}{3} + \frac{\pi}{24}$$
$$x_{2} = \frac{\pi n}{3} + \frac{\pi}{8}$$
Rapid solution
[src]
pi
x1 = --
24
$$x_{1} = \frac{\pi}{24}$$
pi
x2 = --
8
$$x_{2} = \frac{\pi}{8}$$
x2 = pi/8
Sum and product of roots
[src]
sum
pi pi -- + -- 24 8
$$\frac{\pi}{24} + \frac{\pi}{8}$$
=
pi -- 6
$$\frac{\pi}{6}$$
product
pi pi --*-- 24 8
$$\frac{\pi}{24} \frac{\pi}{8}$$
=
2 pi --- 192
$$\frac{\pi^{2}}{192}$$
pi^2/192
Numerical answer
[src]
x1 = -87.8336946066146
x2 = -95.9494756283883
x3 = -3.79609112308767
x4 = 88.0954939944138
x5 = 4.31968989868597
x6 = -43.8513974563575
x7 = 77.885317870247
x8 = -81.2887099116359
x9 = -15.5770635740494
x10 = 2.22529479629277
x11 = 9.55567765466895
x12 = -66.6279441948835
x13 = -71.8639319508665
x14 = 26.3108384738145
x15 = -100.138265833175
x16 = 66.1043454192852
x17 = 38.0918109247762
x18 = -12.1736715326604
x19 = -1.70169602069447
x20 = 46.2075919465499
x21 = 55.8941692951184
x22 = -25.7872396982162
x23 = 40.1862060271694
x24 = -98.0438707307815
x25 = -73.9583270532597
x26 = -29.9760299030026
x27 = -10.0792764302673
x28 = -37.3064127613788
x29 = -32.0704250053958
x30 = -27.8816348006094
x31 = -41.7570023539643
x32 = -51.9671784781312
x33 = 50.3963821513363
x34 = -91.7606854236019
x35 = 60.0829594999048
x36 = -76.0527221556529
x37 = -78.1471172580461
x38 = -81.550509299435
x39 = -17.6714586764426
x40 = 84.1685031774265
x41 = 82.0741080750334
x42 = -85.7392995042214
x43 = -23.692844595823
x44 = -54.0615735805244
x45 = -63.7481509290929
x46 = 48.3019870489431
x47 = -56.4177680707167
x48 = 11.9118721448613
x49 = 94.3786793015934
x50 = -49.872783375738
x51 = -34.164820107789
x52 = 12.6972703082587
x53 = 79.9797129726402
x54 = -5.89048622548086
x55 = 70.2931356240716
x56 = 53.7997741927252
x57 = 68.1987405216784
x58 = -65.8425460314861
x59 = -59.2975613365073
x60 = 86.0010988920206
x61 = 53.5379748049261
x62 = -47.7783882733448
x63 = 16.1006623496477
x64 = -7.98488132787406
x65 = 92.2842841992002
x66 = 99.8764664453755
x67 = 72.3875307264648
x68 = -69.7695368484733
x69 = 24.2164433714213
x70 = -83.6449044018282
x71 = 18.1950574520409
x72 = 20.2894525544341
x73 = -21.860248881229
x74 = -19.7658537788358
x75 = 31.5468262297975
x76 = -60.3447588877039
x77 = -61.6537558266997
x78 = 661.959752050149
x79 = -39.6626072515711
x80 = 14.0062672472545
x81 = 35.997415822383
x82 = -248.054919939694
x83 = 64.2717497046912
x84 = 42.2806011295626
x85 = 6.41408500107916
x86 = 62.177354602298
x87 = 240.20093830572
x88 = 74.7437252166572
x89 = 0.130899693899575
x90 = 22.1220482690281
x91 = 44.1131968441567
x92 = 28.4052335762077
x93 = -93.8550805259951
x94 = 90.189889096807
x95 = 33.9030207199899
x96 = -56.1559686829176
x97 = 57.9885643975116
x97 = 57.9885643975116