Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 3x-2(3x+4)=10
-
Equation tan(x)=-1/2
-
Equation x/3+x/12=15/4
-
Equation 2^x=16
- Express {x} in terms of y where:
- 3*x-7*y=13
- 6*x-17*y=-12
- -3*x+17*y=-5
- 17*x-20*y=-12
-
Identical expressions
- two *sin(x)-sqrt(two)= zero
- 2 multiply by sinus of (x) minus square root of (2) equally 0
- two multiply by sinus of (x) minus square root of (two) equally zero
- 2*sin(x)-√(2)=0
- 2sin(x)-sqrt(2)=0
- 2sinx-sqrt2=0
- 2*sin(x)-sqrt(2)=O
-
Similar expressions
- 2*sin(x)+sqrt(2)=0
- 2sin(x)-sqrt(2)*cos(x)=sqrt(2)*sin(x)
- 2*sinx-sqrt(2)=0
2*sin(x)-sqrt(2)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$2 \sin{\left(x \right)} - \sqrt{2} = 0$$
- this is the simplest trigonometric equation
We get:
$$2 \sin{\left(x \right)} = \sqrt{2}$$
The equation is transformed to
$$\sin{\left(x \right)} = \frac{\sqrt{2}}{2}$$
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
$$2 \sin{\left(x \right)} - \sqrt{2} = 0$$
- this is the simplest trigonometric equation
Move -sqrt(2) to right part of the equation
with the change of sign in -sqrt(2)
We get:
$$2 \sin{\left(x \right)} = \sqrt{2}$$
Divide both parts of the equation by 2
The equation is transformed to
$$\sin{\left(x \right)} = \frac{\sqrt{2}}{2}$$
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
x1 = --
4
$$x_{1} = \frac{\pi}{4}$$
3*pi
x2 = ----
4
$$x_{2} = \frac{3 \pi}{4}$$
x2 = 3*pi/4
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
Numerical answer
[src]
x1 = 90.3207887907066
x2 = -99.7455667514759
x3 = -24.3473430653209
x4 = -30.6305283725005
x5 = 76.1836218495525
x6 = -5.49778714378214
x7 = -62.0464549083984
x8 = -73.0420291959627
x9 = -36.9137136796801
x10 = 8.63937979737193
x11 = -41.6261026600648
x12 = -87.1791961371168
x13 = 95.0331777710912
x14 = 38.484510006475
x15 = -237.975643509427
x16 = -85.6083998103219
x17 = -35.3429173528852
x18 = -22.776546738526
x19 = -66.7588438887831
x20 = 2476.36040919215
x21 = -118.595122673015
x22 = -43.1968989868597
x23 = 51.0508806208341
x24 = 0.785398163397448
x25 = -80.8960108299372
x26 = 128.019900633784
x27 = 40.0553063332699
x28 = 52.621676947629
x29 = 69.9004365423729
x30 = 2151.20556954561
x31 = 101.316363078271
x32 = 84.037603483527
x33 = 96.6039740978861
x34 = 13.3517687777566
x35 = 88.7499924639117
x36 = -3.92699081698724
x37 = -68.329640215578
x38 = 58.9048622548086
x39 = -11.7809724509617
x40 = 19.6349540849362
x41 = -55.7632696012188
x42 = -1160.03308733803
x43 = -10.2101761241668
x44 = 27.4889357189107
x45 = -17680.09805624
x46 = 46.3384916404494
x47 = 82.4668071567321
x48 = -93.4623814442964
x49 = -29.0597320457056
x50 = -60.4756585816035
x51 = -186.139364725195
x52 = 71.4712328691678
x53 = 44.7676953136546
x54 = 32.2013246992954
x55 = -91.8915851175014
x56 = -98.174770424681
x57 = -49.4800842940392
x58 = 6964.12551484517
x59 = 65.1880475619882
x60 = -74.6128255227576
x61 = 57.3340659280137
x62 = -79.3252145031423
x63 = -54.1924732744239
x64 = 63.6172512351933
x65 = -18.0641577581413
x66 = 21.2057504117311
x67 = 25.9181393921158
x68 = 77.7544181763474
x69 = 2.35619449019234
x70 = 14.9225651045515
x71 = 7.06858347057703
x72 = -47.9092879672443
x73 = 33.7721210260903
x74 = -16.4933614313464
x74 = -16.4933614313464
The graph