Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 0*x=0
-
Equation x^2=0
-
Equation sin(x)=-√3/2
-
Equation (x+10)(-x-8)=0
- Express {x} in terms of y where:
- 18*x+14*y=-11
- -5*x+6*y=19
- 4*x+16*y=6
- -6*x+1*y=14
- Derivative of:
-
2sinx+1
- Graphing y =:
- 2sinx+1
-
Identical expressions
- 2sinx+ one = zero
- 2 sinus of x plus 1 equally 0
- 2 sinus of x plus one equally zero
- 2sinx+1=O
-
Similar expressions
- (2*x+pi/2)*(2*sin(x))+1=0
- 2sinx-1=0
- cos(2*x)+sqrt(2)*sin(x)+1=0
- cos(x)+sqrt((2-sqrt(2))/2)*(sinx+1)=0
- (sqrt2*sin(x)+1)*(sqrt(-5cos(x)))=0
2sinx+1=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$2 \sin{\left(x \right)} + 1 = 0$$
- this is the simplest trigonometric equation
We get:
$$2 \sin{\left(x \right)} = -1$$
The equation is transformed to
$$\sin{\left(x \right)} = - \frac{1}{2}$$
This equation is transformed to
$$x = 2 \pi n + \operatorname{asin}{\left(- \frac{1}{2} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(- \frac{1}{2} \right)} + \pi$$
Or
$$x = 2 \pi n - \frac{\pi}{6}$$
$$x = 2 \pi n + \frac{7 \pi}{6}$$
, where n - is a integer
$$2 \sin{\left(x \right)} + 1 = 0$$
- this is the simplest trigonometric equation
Move 1 to right part of the equation
with the change of sign in 1
We get:
$$2 \sin{\left(x \right)} = -1$$
Divide both parts of the equation by 2
The equation is transformed to
$$\sin{\left(x \right)} = - \frac{1}{2}$$
This equation is transformed to
$$x = 2 \pi n + \operatorname{asin}{\left(- \frac{1}{2} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(- \frac{1}{2} \right)} + \pi$$
Or
$$x = 2 \pi n - \frac{\pi}{6}$$
$$x = 2 \pi n + \frac{7 \pi}{6}$$
, where n - is a integer
Rapid solution
[src]
-pi
x1 = ----
6
$$x_{1} = - \frac{\pi}{6}$$
7*pi
x2 = ----
6
$$x_{2} = \frac{7 \pi}{6}$$
Sum and product of roots
[src]
sum
pi 7*pi
0 - -- + ----
6 6
$$\left(- \frac{\pi}{6} + 0\right) + \frac{7 \pi}{6}$$
=
pi
$$\pi$$
product
-pi 7*pi 1*----*---- 6 6
$$\frac{7 \pi}{6} \cdot 1 \left(- \frac{\pi}{6}\right)$$
=
2 -7*pi ------ 36
$$- \frac{7 \pi^{2}}{36}$$
-7*pi^2/36
Numerical answer
[src]
x1 = 24.60914245312
x2 = 16.2315620435473
x3 = 97.9129710368819
x4 = 79.0634151153431
x5 = 53.9306738866248
x6 = -63.3554518473942
x7 = -13.0899693899575
x8 = 72.7802298081635
x9 = -0.523598775598299
x10 = -15.1843644923507
x11 = 74.8746249105567
x12 = -96.8657734856853
x13 = 66400.1787274983
x14 = -19.3731546971371
x15 = 91.6297857297023
x16 = 192.160750644576
x17 = 12.0427718387609
x18 = -50.789081233035
x19 = -34.0339204138894
x20 = 87.4409955249159
x21 = -8.90117918517108
x22 = 437.20497762458
x23 = -75.9218224617533
x24 = 28.7979326579064
x25 = 68.5914396033772
x26 = 49.7418836818384
x27 = 93.7241808320955
x28 = -82.2050077689329
x29 = -88.4881930761125
x30 = -52.8834763354282
x31 = -101.054563690472
x32 = -40.317105721069
x33 = 9.94837673636768
x34 = 56.025068989018
x35 = -65.4498469497874
x36 = -57.0722665402146
x37 = 62.3082542961976
x38 = 35.081117965086
x39 = -71.733032256967
x40 = -59.1666616426078
x41 = -195.302343298165
x42 = -38.2227106186758
x43 = -25.6563400043166
x44 = -90.5825881785057
x45 = 60.2138591938044
x46 = 81.1578102177363
x47 = -27.7507351067098
x48 = -94.7713783832921
x49 = 41.3643032722656
x50 = -6.80678408277789
x51 = -44.5058959258554
x52 = -69.6386371545737
x53 = 3.66519142918809
x54 = -31.9395253114962
x55 = 43.4586983746588
x56 = 30.8923277602996
x57 = 66.497044500984
x58 = -78.0162175641465
x59 = 85.3466004225227
x60 = -84.2994028713261
x61 = 100.007366139275
x62 = -151.320046147908
x63 = 22.5147473507269
x64 = -2.61799387799149
x65 = 18.3259571459405
x66 = -46.6002910282486
x67 = -21.4675497995303
x68 = 5.75958653158129
x69 = 47.6474885794452
x70 = 37.1755130674792
x70 = 37.1755130674792
The graph