Mister Exam
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How to use it?
- Equation:
-
Equation sin(4*x)=-sqrt(2)/2
- Equation sin5xcos3x-cos5xsin3x=-(sqrt(3)/2)
-
Equation 4sin^3(x)+3sinx+4sqrt(3)=4sqrt(3)*cos^2(x)
-
Equation tgx=0
- Express {x} in terms of y where:
- 15*x-15*y=16
- (x^2+y^2-1)^3+x^2*y^3=0
- 4*x-16*y=6
- -1*x-19*y=-10
- Derivative of:
-
sin(4*x)
- Graphing y =:
-
sin(4*x)
- Limit of the function:
-
sin(4*x)
-
Identical expressions
- sin(four *x)=-sqrt(two)/ two
- sinus of (4 multiply by x) equally minus square root of (2) divide by 2
- sinus of (four multiply by x) equally minus square root of (two) divide by two
- sin(4*x)=-√(2)/2
- sin(4x)=-sqrt(2)/2
- sin4x=-sqrt2/2
- sin(4*x)=-sqrt(2) divide by 2
-
Similar expressions
- cos*((pi(4x+48))/4)=-(sqrt(2)/2)
- 2cos^2(2x)-2sin(4x)+1=0
- sin4x=1
- sinx/4=-sqrt2/2
- sin(4*x)=+sqrt(2)/2
- 2sinxcos3x+sin4x=0
sin(4*x)=-sqrt(2)/2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
___
-\/ 2
sin(4*x) = -------
2
$$\sin{\left(4 x \right)} = \frac{\left(-1\right) \sqrt{2}}{2}$$
Detail solution
Given the equation
$$\sin{\left(4 x \right)} = \frac{\left(-1\right) \sqrt{2}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$4 x = 2 \pi n + \operatorname{asin}{\left(- \frac{\sqrt{2}}{2} \right)}$$
$$4 x = 2 \pi n - \operatorname{asin}{\left(- \frac{\sqrt{2}}{2} \right)} + \pi$$
Or
$$4 x = 2 \pi n - \frac{\pi}{4}$$
$$4 x = 2 \pi n + \frac{5 \pi}{4}$$
, where n - is a integer
Divide both parts of the equation by
$$4$$
we get the answer:
$$x_{1} = \frac{\pi n}{2} - \frac{\pi}{16}$$
$$x_{2} = \frac{\pi n}{2} + \frac{5 \pi}{16}$$
$$\sin{\left(4 x \right)} = \frac{\left(-1\right) \sqrt{2}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$4 x = 2 \pi n + \operatorname{asin}{\left(- \frac{\sqrt{2}}{2} \right)}$$
$$4 x = 2 \pi n - \operatorname{asin}{\left(- \frac{\sqrt{2}}{2} \right)} + \pi$$
Or
$$4 x = 2 \pi n - \frac{\pi}{4}$$
$$4 x = 2 \pi n + \frac{5 \pi}{4}$$
, where n - is a integer
Divide both parts of the equation by
$$4$$
we get the answer:
$$x_{1} = \frac{\pi n}{2} - \frac{\pi}{16}$$
$$x_{2} = \frac{\pi n}{2} + \frac{5 \pi}{16}$$
Rapid solution
[src]
-pi
x_1 = ----
16
$$x_{1} = - \frac{\pi}{16}$$
5*pi
x_2 = ----
16
$$x_{2} = \frac{5 \pi}{16}$$
Sum and product of roots
[src]
sum
-pi 5*pi ---- + ---- 16 16
$$\left(- \frac{\pi}{16}\right) + \left(\frac{5 \pi}{16}\right)$$
=
pi -- 4
$$\frac{\pi}{4}$$
product
-pi 5*pi ---- * ---- 16 16
$$\left(- \frac{\pi}{16}\right) * \left(\frac{5 \pi}{16}\right)$$
=
2 -5*pi ------ 256
$$- \frac{5 \pi^{2}}{256}$$
Numerical answer
[src]
x1 = 94.0514300668444
x2 = -10.0138265833175
x3 = 90.5171383315559
x4 = -30.0414797499524
x5 = -23.7582944427728
x6 = 33.9684705669396
x7 = -45.7494430179014
x8 = 70.0967860832223
x9 = -91.6952355766521
x10 = -67.7405915930299
x11 = -14.7262155637022
x12 = 99.9419162923253
x13 = 42.2151512826128
x14 = -90.1244392498572
x15 = -52.0326283250809
x16 = -37.8954613839269
x17 = -59.8866099590554
x18 = -17.8678082172919
x19 = -39.8589567924205
x20 = 72.0602814917159
x21 = 227.176418762712
x22 = 79.9142631256904
x23 = 46.5348411812988
x24 = -77.558068635498
x25 = -1.76714586764426
x26 = 40.2516558741192
x27 = -75.9872723087031
x28 = 109.366694253095
x29 = 29.2560815865549
x30 = -3.73064127613788
x31 = -97.9784208838317
x32 = -36.7173641388307
x33 = 48.1056375080937
x34 = -69.7040870015235
x35 = -32.004975158446
x36 = -11.5846229101124
x37 = -44.1786466911065
x38 = 51.2472301616835
x39 = -88.1609438413636
x40 = -99.5492172106266
x41 = 77.9507677171967
x42 = -96.0149254753381
x43 = 86.1974484328699
x44 = 68.5259897564274
x45 = 54.3888228152733
x46 = 28.0779843414588
x47 = -80.3069622073891
x48 = -58.3158136322605
x49 = 2.55254403104171
x50 = 26.1144889329652
x51 = 92.0879346583508
x52 = 57.9231145505618
x53 = -85.0193511877738
x54 = 10.4065256650162
x55 = 65.7770961845363
x56 = -63.0282026126452
x57 = 13.9408174003047
x58 = 84.6266521060751
x59 = 98.3711199655304
x60 = 62.6355035309465
x61 = 24.5436926061703
x62 = 87.7682447596649
x63 = 35.9319659754333
x64 = -94.4441291485432
x65 = -89.7317401681585
x66 = -83.8412539426776
x67 = 11.9773219918111
x68 = 50.0691329165873
x69 = 76.3799713904018
x70 = 62.2428044492478
x71 = -25.7217898512664
x72 = 21.7947990342792
x73 = 6.08683576633022
x74 = 84.2339530243763
x75 = 197.723987635308
x76 = -53.9961237335746
x77 = 18.2605072989907
x78 = -55.5669200603695
x79 = -33.5757714852409
x80 = -0.196349540849362
x81 = 55.9596191420682
x82 = -61.8501053675491
x83 = 32.3976742401447
x84 = 64.2062998577414
x85 = 43.7859476094077
x86 = -81.877758534184
x87 = -74.0237769002095
x88 = -19.4386045440868
x89 = -66.169795266235
x90 = -15.9043128087983
x91 = 7.2649330114264
x92 = -8.05033117482385
x93 = -47.712938426395
x94 = -22.1874981159779
x95 = 4.1233403578366
x96 = 20.2240027074843
x96 = 20.2240027074843
The graph