Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 31+25x+2x^2=7x-9
-
Equation sin(x)=sqrt2/2
- Equation Cx-1^x*(x-1)=30
- Equation 3y^2+y-24/9-y^2=-2
- Express {x} in terms of y where:
- 9*x+18*y=6
- 15*x-15*y=16
- (x^2+y^2-1)^3+x^2*y^3=0
- 4*x-16*y=6
- Derivative of:
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sin(x)
- Integral of d{x}:
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sin(x)
- Canonical form:
- sin(x)
-
Identical expressions
- sin(x)=sqrt two /2
- sinus of (x) equally square root of 2 divide by 2
- sinus of (x) equally square root of two divide by 2
- sin(x)=√2/2
- sinx=sqrt2/2
- sin(x)=sqrt2 divide by 2
-
Similar expressions
- cos*((pi(4x+48))/4)=-(sqrt(2)/2)
- (2log3*2log3)*(8sinx−√3)−7log3*(8sinx−√3)+6=0
- cos((pi*(x+1))/4)=sqrt(2)/2
- sin(4*x)=-sqrt(2)/2
- 4sin^3(x)+3sinx+4sqrt(3)=4sqrt(3)*cos^2(x)
- sinx=sqrt2/2
sin(x)=sqrt2/2 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
Rapid solution
[src]
pi
x_1 = --
4
$$x_{1} = \frac{\pi}{4}$$
3*pi
x_2 = ----
4
$$x_{2} = \frac{3 \pi}{4}$$
Sum and product of roots
[src]
sum
pi 3*pi -- + ---- 4 4
$$\left(\frac{\pi}{4}\right) + \left(\frac{3 \pi}{4}\right)$$
=
pi
$$\pi$$
product
pi 3*pi -- * ---- 4 4
$$\left(\frac{\pi}{4}\right) * \left(\frac{3 \pi}{4}\right)$$
=
2 3*pi ----- 16
$$\frac{3 \pi^{2}}{16}$$
Numerical answer
[src]
x1 = -85.6083998103219
x2 = 101.316363078271
x3 = -24.3473430653209
x4 = 65.1880475619882
x5 = 40.0553063332699
x6 = 33.7721210260903
x7 = -35.3429173528852
x8 = -74.6128255227576
x9 = -22.776546738526
x10 = -87.1791961371168
x11 = -36.9137136796801
x12 = -66.7588438887831
x13 = -93.4623814442964
x14 = 2151.20556954561
x15 = 25.9181393921158
x16 = -5.49778714378214
x17 = 0.785398163397448
x18 = 8.63937979737193
x19 = -237.975643509427
x20 = -17680.09805624
x21 = -73.0420291959627
x22 = 14.9225651045515
x23 = -16.4933614313464
x24 = 90.3207887907066
x25 = 44.7676953136546
x26 = 32.2013246992954
x27 = -80.8960108299372
x28 = 84.037603483527
x29 = -43.1968989868597
x30 = -47.9092879672443
x31 = 51.0508806208341
x32 = 71.4712328691678
x33 = -62.0464549083984
x34 = 57.3340659280137
x35 = -3.92699081698724
x36 = 19.6349540849362
x37 = 52.621676947629
x38 = -29.0597320457056
x39 = -98.174770424681
x40 = -30.6305283725005
x41 = 95.0331777710912
x42 = -49.4800842940392
x43 = -79.3252145031423
x44 = 88.7499924639117
x45 = 76.1836218495525
x46 = 46.3384916404494
x47 = 77.7544181763474
x48 = 6964.12551484517
x49 = 96.6039740978861
x50 = -55.7632696012188
x51 = 7.06858347057703
x52 = -68.329640215578
x53 = 128.019900633784
x54 = -118.595122673015
x55 = -1160.03308733803
x56 = -10.2101761241668
x57 = -91.8915851175014
x58 = -186.139364725195
x59 = -60.4756585816035
x60 = -41.6261026600648
x61 = 58.9048622548086
x62 = -54.1924732744239
x63 = 27.4889357189107
x64 = 63.6172512351933
x65 = 38.484510006475
x66 = 13.3517687777566
x67 = 21.2057504117311
x68 = -99.7455667514759
x69 = -18.0641577581413
x70 = 2.35619449019234
x71 = 69.9004365423729
x72 = 82.4668071567321
x73 = -11.7809724509617
x74 = 2476.36040919215
x74 = 2476.36040919215
The graph