Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation x^4+2x^2-8=0
- Equation sin(x)=1/sqrt(2)
-
Equation 325+=276+183
-
Equation x^3-3x^2+2x=210
- Express {x} in terms of y where:
- (x^2+y^2-1)^3+x^2*y^3=0
- -1*x-19*y=-10
- 4*x-16*y=6
- 5*x+5*y=20
- Derivative of:
-
sin(x)
-
1/sqrt(2)
- Integral of d{x}:
-
sin(x)
- Canonical form:
- sin(x)
-
Identical expressions
- sin(x)= one /sqrt(two)
- sinus of (x) equally 1 divide by square root of (2)
- sinus of (x) equally one divide by square root of (two)
- sin(x)=1/√(2)
- sinx=1/sqrt2
- sin(x)=1 divide by sqrt(2)
-
Similar expressions
- (cos(2x)-3cos(x)-1)/(sqrt(2sin(x)-1))=0
- sinx=0,13
- (arctan(sqrt(2)tan(x)+1)+arctan(sqrt(2)tan(x)-1))/sqrt(2)-1/(sqrt(2))arctan(tan(2x)/sqrt(2))=0
- 5sin^2*x-12sinx+4=0
- sinx=-1/2
- (2^x^2-1)/(sqrt(2+x)-2)=0
- sinx=1/sqrt(2)
sin(x)=1/sqrt(2) equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
1
sin(x) = 1*-----
___
\/ 2
$$\sin{\left(x \right)} = 1 \cdot \frac{1}{\sqrt{2}}$$
Detail solution
Given the equation
$$\sin{\left(x \right)} = 1 \cdot \frac{1}{\sqrt{2}}$$
- 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
$$\sin{\left(x \right)} = 1 \cdot \frac{1}{\sqrt{2}}$$
- 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
x1 = --
4
$$x_{1} = \frac{\pi}{4}$$
3*pi
x2 = ----
4
$$x_{2} = \frac{3 \pi}{4}$$
Sum and product of roots
[src]
sum
pi 3*pi
0 + -- + ----
4 4
$$\left(0 + \frac{\pi}{4}\right) + \frac{3 \pi}{4}$$
=
pi
$$\pi$$
product
pi 3*pi 1*--*---- 4 4
$$\frac{3 \pi}{4} \cdot 1 \frac{\pi}{4}$$
=
2 3*pi ----- 16
$$\frac{3 \pi^{2}}{16}$$
3*pi^2/16
Numerical answer
[src]
x1 = 84.037603483527
x2 = 46.3384916404494
x3 = -99.7455667514759
x4 = 128.019900633784
x5 = 0.785398163397448
x6 = 52.621676947629
x7 = 14.9225651045515
x8 = 6964.12551484517
x9 = 44.7676953136546
x10 = 57.3340659280137
x11 = -54.1924732744239
x12 = 7.06858347057703
x13 = 38.484510006475
x14 = -73.0420291959627
x15 = -24.3473430653209
x16 = -1160.03308733803
x17 = 40.0553063332699
x18 = -60.4756585816035
x19 = 25.9181393921158
x20 = 2476.36040919215
x21 = -17680.09805624
x22 = -49.4800842940392
x23 = 63.6172512351933
x24 = 2.35619449019234
x25 = -186.139364725195
x26 = -36.9137136796801
x27 = -22.776546738526
x28 = 2151.20556954561
x29 = -35.3429173528852
x30 = 21.2057504117311
x31 = 90.3207887907066
x32 = 71.4712328691678
x33 = -237.975643509427
x34 = -118.595122673015
x35 = -80.8960108299372
x36 = 33.7721210260903
x37 = 69.9004365423729
x38 = -47.9092879672443
x39 = -29.0597320457056
x40 = -41.6261026600648
x41 = -62.0464549083984
x42 = -66.7588438887831
x43 = 95.0331777710912
x44 = 32.2013246992954
x45 = -3.92699081698724
x46 = -79.3252145031423
x47 = 96.6039740978861
x48 = -74.6128255227576
x49 = -11.7809724509617
x50 = 76.1836218495525
x51 = 13.3517687777566
x52 = 8.63937979737193
x53 = 27.4889357189107
x54 = 77.7544181763474
x55 = -30.6305283725005
x56 = -85.6083998103219
x57 = -98.174770424681
x58 = -55.7632696012188
x59 = 19.6349540849362
x60 = -87.1791961371168
x61 = -16.4933614313464
x62 = 88.7499924639117
x63 = -68.329640215578
x64 = -43.1968989868597
x65 = -18.0641577581413
x66 = -10.2101761241668
x67 = 58.9048622548086
x68 = 51.0508806208341
x69 = -93.4623814442964
x70 = 65.1880475619882
x71 = -91.8915851175014
x72 = 82.4668071567321
x73 = 101.316363078271
x74 = -5.49778714378214
x74 = -5.49778714378214