Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 4*x=0
-
Equation 7*x=0
-
Equation 4x+3(x-7)=5
- Equation z^3=i
- Express {x} in terms of y where:
- 14*x-17*y=-4
- 18*x-10*y=-9
- 10*x+14*y=1
- 6*x+16*y=-7
- Derivative of:
- sqrt(2)
- Integral of d{x}:
-
sqrt(2)
- sqrt(2)
-
Identical expressions
- two *(sin(two x))=sqrt(2)
- 2 multiply by ( sinus of (2x)) equally square root of (2)
- two multiply by ( sinus of (two x)) equally square root of (2)
- 2*(sin(2x))=√(2)
- 2(sin(2x))=sqrt(2)
- 2sin2x=sqrt2
-
Similar expressions
- sqrt(2x+1)=4
- 2sin^2(x)-9cosx-6=0
- sin(x)+sqrt3*cosx=2sin2x
- (2sin^2xcosx)/sinx=0
- 1+3cos2x=2sin2x
- sqrt(x)-4/(sqrt(2+x))+sqrt(2+x)=0
2*(sin(2x))=sqrt(2) equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$2 \sin{\left(2 x \right)} = \sqrt{2}$$
- this is the simplest trigonometric equation
The equation is transformed to
$$\sin{\left(2 x \right)} = \frac{\sqrt{2}}{2}$$
This equation is transformed to
$$2 x = 2 \pi n + \operatorname{asin}{\left(\frac{\sqrt{2}}{2} \right)}$$
$$2 x = 2 \pi n - \operatorname{asin}{\left(\frac{\sqrt{2}}{2} \right)} + \pi$$
Or
$$2 x = 2 \pi n + \frac{\pi}{4}$$
$$2 x = 2 \pi n + \frac{3 \pi}{4}$$
, where n - is a integer
Divide both parts of the equation by
$$2$$
we get the answer:
$$x_{1} = \pi n + \frac{\pi}{8}$$
$$x_{2} = \pi n + \frac{3 \pi}{8}$$
$$2 \sin{\left(2 x \right)} = \sqrt{2}$$
- this is the simplest trigonometric equation
Divide both parts of the equation by 2
The equation is transformed to
$$\sin{\left(2 x \right)} = \frac{\sqrt{2}}{2}$$
This equation is transformed to
$$2 x = 2 \pi n + \operatorname{asin}{\left(\frac{\sqrt{2}}{2} \right)}$$
$$2 x = 2 \pi n - \operatorname{asin}{\left(\frac{\sqrt{2}}{2} \right)} + \pi$$
Or
$$2 x = 2 \pi n + \frac{\pi}{4}$$
$$2 x = 2 \pi n + \frac{3 \pi}{4}$$
, where n - is a integer
Divide both parts of the equation by
$$2$$
we get the answer:
$$x_{1} = \pi n + \frac{\pi}{8}$$
$$x_{2} = \pi n + \frac{3 \pi}{8}$$
Rapid solution
[src]
pi
x1 = --
8
$$x_{1} = \frac{\pi}{8}$$
3*pi
x2 = ----
8
$$x_{2} = \frac{3 \pi}{8}$$
x2 = 3*pi/8
Sum and product of roots
[src]
sum
pi 3*pi -- + ---- 8 8
$$\frac{\pi}{8} + \frac{3 \pi}{8}$$
=
pi -- 2
$$\frac{\pi}{2}$$
product
pi 3*pi --*---- 8 8
$$\frac{\pi}{8} \frac{3 \pi}{8}$$
=
2 3*pi ----- 64
$$\frac{3 \pi^{2}}{64}$$
3*pi^2/64
Numerical answer
[src]
x1 = -36.5210145979813
x2 = -99.3528676697772
x3 = 31.8086256175967
x4 = 50.6581815391354
x5 = -55.3705705195201
x6 = 100.923663996572
x7 = -52.2289778659303
x8 = 72.649330114264
x9 = 4622.46089067568
x10 = -23.9546439836222
x11 = -74.2201264410589
x12 = -8.24668071567321
x13 = -78.1471172580461
x14 = 97.7820713429823
x15 = 28.6670329640069
x16 = 7.46128255227576
x17 = -37.3064127613788
x18 = 12.9590696960579
x19 = -5901.87449885013
x20 = -87.5718952188155
x21 = 89.1426915456104
x22 = 48.3019870489431
x23 = -17.6714586764426
x24 = 104.850654813559
x25 = -89.9280897090078
x26 = -56.1559686829176
x27 = 26.3108384738145
x28 = -31.0232274541992
x29 = 6.67588438887831
x30 = 27323.6094055155
x31 = 95.42587685279
x32 = -49.872783375738
x33 = 34.9502182711865
x34 = -53.0143760293278
x35 = -1.96349540849362
x36 = 64.009950316892
x37 = 79.717913584841
x38 = -75.0055246044563
x39 = -100.138265833175
x40 = -21.5984494934298
x41 = 9.8174770424681
x42 = 20.0276531666349
x43 = 88.3572933822129
x44 = 75.7909227678538
x45 = -14.5298660228528
x46 = 92.2842841992002
x47 = -61.6537558266997
x48 = -93.8550805259951
x49 = 73.4347282776614
x50 = -81.2887099116359
x51 = -34.164820107789
x52 = 60.0829594999048
x53 = 16.1006623496477
x54 = -43.5895980685584
x55 = -9.03207887907065
x56 = 35.7356164345839
x57 = 66.3661448070844
x58 = 13.7444678594553
x59 = 70.2931356240716
x60 = -67.9369411338793
x61 = 29.4524311274043
x62 = 4.31968989868597
x63 = -65.5807466436869
x64 = 82.0741080750334
x65 = 44.3749962319558
x66 = 51.4435797025329
x67 = -27.8816348006094
x68 = 0.392699081698724
x69 = 56.941366846315
x70 = -80.5033117482384
x71 = 38.0918109247762
x72 = -96.2112750161874
x73 = 53.7997741927252
x74 = -45.9457925587507
x75 = 94.6404786893925
x76 = 78.9325154214436
x77 = -58.5121631731099
x78 = -59.2975613365073
x79 = 22.3838476568273
x80 = 57.7267650097125
x81 = 86.0010988920206
x82 = -12.1736715326604
x83 = -83.6449044018282
x84 = 42.0188017417635
x85 = -39.6626072515711
x86 = -30.2378292908018
x87 = -15.3152641862502
x88 = -5.89048622548086
x89 = -71.8639319508665
x89 = -71.8639319508665