Mister Exam
Other calculators
-
How to use it?
- Equation:
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Equation 4-6*(x+2)=3-5*x
-
Equation 4-6(x+2)=3-5x
-
Equation 1+sin(x)=0
-
Equation x^2-3*x+1=0
- Express {x} in terms of y where:
- 18*x-8*y=-2
- -11*x+15*y=7
- 6*x+17*y=3
- 1*x+10*y=-18
- Derivative of:
-
sin(x)
- Integral of d{x}:
-
sin(x)
- Canonical form:
- sin(x)
- Limit of the function:
-
sqrt(2)/2
- sqrt(2)/2
-
Identical expressions
- sin(x)=sqrt(two)/ two
- sinus of (x) equally square root of (2) divide by 2
- sinus of (x) equally square root of (two) divide by two
- sin(x)=√(2)/2
- sinx=sqrt2/2
- sin(x)=sqrt(2) divide by 2
-
Similar expressions
- sin(x+pi*1/3)=sqrt(3)/2
- sinpi(2x-5)/2=-sqrt2/2
- sinx=sqrt(2)/2
sin(x)=sqrt(2)/2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sin{\left(x \right)} = \frac{\sqrt{2}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{\sqrt{2}}{2} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{\sqrt{2}}{2} \right)} + \pi$$
Or
$$x = 2 \pi n + \frac{\pi}{4}$$
$$x = 2 \pi n + \frac{3 \pi}{4}$$
, where n - is a integer
$$\sin{\left(x \right)} = \frac{\sqrt{2}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{\sqrt{2}}{2} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{\sqrt{2}}{2} \right)} + \pi$$
Or
$$x = 2 \pi n + \frac{\pi}{4}$$
$$x = 2 \pi n + \frac{3 \pi}{4}$$
, where n - is a integer
Sum and product of roots
[src]
sum
pi 3*pi -- + ---- 4 4
$$\frac{\pi}{4} + \frac{3 \pi}{4}$$
=
pi
$$\pi$$
product
pi 3*pi --*---- 4 4
$$\frac{\pi}{4} \frac{3 \pi}{4}$$
=
2 3*pi ----- 16
$$\frac{3 \pi^{2}}{16}$$
3*pi^2/16
Rapid solution
[src]
pi
x1 = --
4
$$x_{1} = \frac{\pi}{4}$$
3*pi
x2 = ----
4
$$x_{2} = \frac{3 \pi}{4}$$
x2 = 3*pi/4
Numerical answer
[src]
x1 = 27.4889357189107
x2 = 95.0331777710912
x3 = 32.2013246992954
x4 = 90.3207887907066
x5 = -66.7588438887831
x6 = -49.4800842940392
x7 = 69.9004365423729
x8 = 38.484510006475
x9 = -29.0597320457056
x10 = -60.4756585816035
x11 = -93.4623814442964
x12 = -1160.03308733803
x13 = 14.9225651045515
x14 = 2476.36040919215
x15 = -79.3252145031423
x16 = -35.3429173528852
x17 = -237.975643509427
x18 = 76.1836218495525
x19 = -98.174770424681
x20 = -18.0641577581413
x21 = -118.595122673015
x22 = 33.7721210260903
x23 = 101.316363078271
x24 = -85.6083998103219
x25 = -54.1924732744239
x26 = 51.0508806208341
x27 = 8.63937979737193
x28 = 58.9048622548086
x29 = -87.1791961371168
x30 = 40.0553063332699
x31 = -186.139364725195
x32 = -17680.09805624
x33 = 44.7676953136546
x34 = -99.7455667514759
x35 = -47.9092879672443
x36 = 13.3517687777566
x37 = -91.8915851175014
x38 = -41.6261026600648
x39 = 84.037603483527
x40 = 96.6039740978861
x41 = -68.329640215578
x42 = 2.35619449019234
x43 = 6964.12551484517
x44 = -24.3473430653209
x45 = -5.49778714378214
x46 = -73.0420291959627
x47 = 82.4668071567321
x48 = 71.4712328691678
x49 = 0.785398163397448
x50 = 65.1880475619882
x51 = 25.9181393921158
x52 = -10.2101761241668
x53 = 2151.20556954561
x54 = 57.3340659280137
x55 = -16.4933614313464
x56 = 77.7544181763474
x57 = -30.6305283725005
x58 = -36.9137136796801
x59 = 46.3384916404494
x60 = -43.1968989868597
x61 = -80.8960108299372
x62 = 88.7499924639117
x63 = -55.7632696012188
x64 = 21.2057504117311
x65 = -3.92699081698724
x66 = -62.0464549083984
x67 = -22.776546738526
x68 = 128.019900633784
x69 = 19.6349540849362
x70 = 7.06858347057703
x71 = -74.6128255227576
x72 = 52.621676947629
x73 = 63.6172512351933
x74 = -11.7809724509617
x74 = -11.7809724509617
The graph