Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 2x-5=7
-
Equation x^4=(2*x-3)^2
-
Equation cos(x)=-sqrt(3)/2
-
Equation cos(x)=0
- Express {x} in terms of y where:
- 4*x+3*y=-15
- -16*x+7*y=-5
- (x^2+y^2-1)^3-x^2*y^3=0
- -2*x+1*y=-8
- Derivative of:
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cos(x)
- Graphing y =:
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cos(x)
- Integral of d{x}:
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cos(x)
-
Identical expressions
- cos(x)=-sqrt(three)/ two
- co sinus of e of (x) equally minus square root of (3) divide by 2
- co sinus of e of (x) equally minus square root of (three) divide by two
- cos(x)=-√(3)/2
- cosx=-sqrt3/2
- cos(x)=-sqrt(3) divide by 2
-
Similar expressions
- cos(x)=+sqrt(3)/2
- sqrt(((2-sqrt(3))/2)*(1+cos(x)))+sin(x)=1
- 4sqrt((1-((sqrt(3))/2))/(6x+6))+pi/(6x+6)=1,5*sqrt(3)-2
- (sin(x)-(sqrt(3)/2))*sqrt(3*x^2-7*x+4)=0
- 2sin^2x+7cosx-5=0
- cosx=-sqrt(3)/2
cos(x)=-sqrt(3)/2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
___
-\/ 3
cos(x) = -------
2
$$\cos{\left(x \right)} = \frac{\left(-1\right) \sqrt{3}}{2}$$
Detail solution
Given the equation
$$\cos{\left(x \right)} = \frac{\left(-1\right) \sqrt{3}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{acos}{\left(- \frac{\sqrt{3}}{2} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(- \frac{\sqrt{3}}{2} \right)}$$
Or
$$x = \pi n + \frac{5 \pi}{6}$$
$$x = \pi n - \frac{\pi}{6}$$
, where n - is a integer
$$\cos{\left(x \right)} = \frac{\left(-1\right) \sqrt{3}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{acos}{\left(- \frac{\sqrt{3}}{2} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(- \frac{\sqrt{3}}{2} \right)}$$
Or
$$x = \pi n + \frac{5 \pi}{6}$$
$$x = \pi n - \frac{\pi}{6}$$
, where n - is a integer
Sum and product of roots
[src]
sum
5*pi 7*pi ---- + ---- 6 6
$$\frac{5 \pi}{6} + \frac{7 \pi}{6}$$
=
2*pi
$$2 \pi$$
product
5*pi 7*pi ----*---- 6 6
$$\frac{5 \pi}{6} \frac{7 \pi}{6}$$
=
2 35*pi ------ 36
$$\frac{35 \pi^{2}}{36}$$
35*pi^2/36
Rapid solution
[src]
5*pi
x1 = ----
6
$$x_{1} = \frac{5 \pi}{6}$$
7*pi
x2 = ----
6
$$x_{2} = \frac{7 \pi}{6}$$
x2 = 7*pi/6
Numerical answer
[src]
x1 = -21.4675497995303
x2 = -65.4498469497874
x3 = -46.6002910282486
x4 = -79.0634151153431
x5 = -41.3643032722656
x6 = -2.61799387799149
x7 = -9.94837673636768
x8 = -28.7979326579064
x9 = 22.5147473507269
x10 = 15.1843644923507
x11 = -97.9129710368819
x12 = -96.8657734856853
x13 = -35.081117965086
x14 = 2.61799387799149
x15 = -47.6474885794452
x16 = 192.160750644576
x17 = -15.1843644923507
x18 = -34.0339204138894
x19 = 72.7802298081635
x20 = 3.66519142918809
x21 = -71.733032256967
x22 = -53.9306738866248
x23 = -90.5825881785057
x24 = 59.1666616426078
x25 = 47.6474885794452
x26 = -40.317105721069
x27 = 28.7979326579064
x28 = -8.90117918517108
x29 = 46.6002910282486
x30 = 27.7507351067098
x31 = -78.0162175641465
x32 = 97.9129710368819
x33 = 96.8657734856853
x34 = -52.8834763354282
x35 = -16.2315620435473
x36 = 78.0162175641465
x37 = 84.2994028713261
x38 = 34.0339204138894
x39 = -59.1666616426078
x40 = 9.94837673636768
x41 = -22.5147473507269
x42 = -66.497044500984
x43 = 40.317105721069
x44 = 53.9306738866248
x45 = 79.0634151153431
x46 = -4697.20461589234
x47 = -3.66519142918809
x48 = 21.4675497995303
x49 = 35.081117965086
x50 = 41.3643032722656
x51 = -128.281700021583
x52 = 71.733032256967
x53 = 216.246294322097
x54 = 8.90117918517108
x55 = 52.8834763354282
x56 = 85.3466004225227
x57 = 16.2315620435473
x58 = -91.6297857297023
x59 = 91.6297857297023
x60 = -27.7507351067098
x61 = -72.7802298081635
x62 = 60.2138591938044
x63 = -857.131195654415
x64 = -60.2138591938044
x65 = 203.679923707738
x66 = 65.4498469497874
x67 = 90.5825881785057
x68 = -85.3466004225227
x69 = 66.497044500984
x70 = -84.2994028713261
x70 = -84.2994028713261
The graph