Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation (x-4)^2+(x+9)^2=2*x^2
-
Equation 9-2(-4x+7)=7
-
Equation sin(x)+1/2=0
-
Equation 4^x-12*2^x+32=0
- Express {x} in terms of y where:
- -11*x+4*y=-8
- -14*x+1*y=3
- 14*x+16*y=14
- 16*x+7*y=8
- Derivative of:
- sin(x)+1/2
-
Identical expressions
- sin(x)+ one / two = zero
- sinus of (x) plus 1 divide by 2 equally 0
- sinus of (x) plus one divide by two equally zero
- sinx+1/2=0
- sin(x)+1/2=O
- sin(x)+1 divide by 2=0
-
Similar expressions
- sin(x)-1/2=0
- sinx+1/2=cosx+1/2
- (2*sinx+1)/(2*cosx-sqrt3)=0
- sinx+1/2*sin2x=0
- sinx+1/2=0
sin(x)+1/2=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sin{\left(x \right)} + \frac{1}{2} = 0$$
- this is the simplest trigonometric equation
We get:
$$\sin{\left(x \right)} = - \frac{1}{2}$$
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
$$\sin{\left(x \right)} + \frac{1}{2} = 0$$
- this is the simplest trigonometric equation
Move 1/2 to right part of the equation
with the change of sign in 1/2
We get:
$$\sin{\left(x \right)} = - \frac{1}{2}$$
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
$$x_{2} = \frac{7 \pi}{6}$$
x2 = 7*pi/6
Sum and product of roots
[src]
sum
pi 7*pi - -- + ---- 6 6
$$- \frac{\pi}{6} + \frac{7 \pi}{6}$$
=
pi
$$\pi$$
product
-pi 7*pi ----*---- 6 6
$$- \frac{\pi}{6} \frac{7 \pi}{6}$$
=
2 -7*pi ------ 36
$$- \frac{7 \pi^{2}}{36}$$
-7*pi^2/36
Numerical answer
[src]
x1 = -21.4675497995303
x2 = -65.4498469497874
x3 = 87.4409955249159
x4 = -46.6002910282486
x5 = 93.7241808320955
x6 = 30.8923277602996
x7 = -2.61799387799149
x8 = -38.2227106186758
x9 = 22.5147473507269
x10 = -88.4881930761125
x11 = -96.8657734856853
x12 = 43.4586983746588
x13 = -101.054563690472
x14 = -19.3731546971371
x15 = 66400.1787274983
x16 = 192.160750644576
x17 = -15.1843644923507
x18 = -34.0339204138894
x19 = 56.025068989018
x20 = 72.7802298081635
x21 = 3.66519142918809
x22 = 62.3082542961976
x23 = -71.733032256967
x24 = -90.5825881785057
x25 = -40.317105721069
x26 = -25.6563400043166
x27 = 47.6474885794452
x28 = 28.7979326579064
x29 = -0.523598775598299
x30 = -8.90117918517108
x31 = -151.320046147908
x32 = -13.0899693899575
x33 = -78.0162175641465
x34 = 97.9129710368819
x35 = -57.0722665402146
x36 = -52.8834763354282
x37 = -50.789081233035
x38 = 437.20497762458
x39 = -59.1666616426078
x40 = -31.9395253114962
x41 = 49.7418836818384
x42 = 18.3259571459405
x43 = 81.1578102177363
x44 = 24.60914245312
x45 = 9.94837673636768
x46 = 68.5914396033772
x47 = -69.6386371545737
x48 = 53.9306738866248
x49 = 74.8746249105567
x50 = 79.0634151153431
x51 = -63.3554518473942
x52 = -6.80678408277789
x53 = 35.081117965086
x54 = 41.3643032722656
x55 = -75.9218224617533
x56 = 12.0427718387609
x57 = 16.2315620435473
x58 = -82.2050077689329
x59 = -27.7507351067098
x60 = 91.6297857297023
x61 = 60.2138591938044
x62 = 5.75958653158129
x63 = -44.5058959258554
x64 = -195.302343298165
x65 = 37.1755130674792
x66 = 100.007366139275
x67 = 85.3466004225227
x68 = 66.497044500984
x69 = -94.7713783832921
x70 = -84.2994028713261
x70 = -84.2994028713261
The graph