Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 5-2(x-1)=4-x
-
Equation x^4=(4x-21)^2
-
Equation cos(pi*(x-1)/3)=1/2
-
Equation 3(5-x)+13=4(3x-8)
- Express {x} in terms of y where:
- 10*x+5*y=-17
- -2*x-14*y=7
- 17*x+16*y=7
- 18*x-14*y=-12
- Derivative of:
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cos(x)
- Graphing y =:
-
cos(x)
- Integral of d{x}:
-
cos(x)
-
Identical expressions
- cos(x)=(-√ three / two)
- co sinus of e of (x) equally ( minus √3 divide by 2)
- co sinus of e of (x) equally ( minus √ three divide by two)
- cosx=-√3/2
- cos(x)=(-√3 divide by 2)
-
Similar expressions
- cos(x)=(√3/2)
- cosx/5=-(√3/2)
- -cos(x)=-(√3/2)
- cos(2x-pi/4)=-√3/2
- sin(-2x-(p/6))=-√3/2
- sinx-cosx=1/2
- cosx=(-√3/2)
cos(x)=(-√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
Rapid solution
[src]
5*pi
x_1 = ----
6
$$x_{1} = \frac{5 \pi}{6}$$
7*pi
x_2 = ----
6
$$x_{2} = \frac{7 \pi}{6}$$
Sum and product of roots
[src]
sum
5*pi 7*pi ---- + ---- 6 6
$$\left(\frac{5 \pi}{6}\right) + \left(\frac{7 \pi}{6}\right)$$
=
2*pi
$$2 \pi$$
product
5*pi 7*pi ---- * ---- 6 6
$$\left(\frac{5 \pi}{6}\right) * \left(\frac{7 \pi}{6}\right)$$
=
2 35*pi ------ 36
$$\frac{35 \pi^{2}}{36}$$
Numerical answer
[src]
x1 = -65.4498469497874
x2 = -857.131195654415
x3 = -46.6002910282486
x4 = 60.2138591938044
x5 = -27.7507351067098
x6 = 84.2994028713261
x7 = -53.9306738866248
x8 = 21.4675497995303
x9 = 3.66519142918809
x10 = -16.2315620435473
x11 = -2.61799387799149
x12 = -15.1843644923507
x13 = -79.0634151153431
x14 = 16.2315620435473
x15 = 71.733032256967
x16 = 216.246294322097
x17 = 53.9306738866248
x18 = -71.733032256967
x19 = -96.8657734856853
x20 = -4697.20461589234
x21 = 78.0162175641465
x22 = 28.7979326579064
x23 = -84.2994028713261
x24 = 40.317105721069
x25 = 79.0634151153431
x26 = -47.6474885794452
x27 = 47.6474885794452
x28 = -52.8834763354282
x29 = -9.94837673636768
x30 = -59.1666616426078
x31 = -3.66519142918809
x32 = 2.61799387799149
x33 = 192.160750644576
x34 = -40.317105721069
x35 = 91.6297857297023
x36 = -8.90117918517108
x37 = 15.1843644923507
x38 = -21.4675497995303
x39 = 85.3466004225227
x40 = -60.2138591938044
x41 = 96.8657734856853
x42 = -41.3643032722656
x43 = -28.7979326579064
x44 = -78.0162175641465
x45 = 90.5825881785057
x46 = 41.3643032722656
x47 = -22.5147473507269
x48 = -97.9129710368819
x49 = 59.1666616426078
x50 = -66.497044500984
x51 = 97.9129710368819
x52 = 34.0339204138894
x53 = 8.90117918517108
x54 = 46.6002910282486
x55 = -91.6297857297023
x56 = -90.5825881785057
x57 = -35.081117965086
x58 = -34.0339204138894
x59 = 66.497044500984
x60 = 203.679923707738
x61 = 9.94837673636768
x62 = 72.7802298081635
x63 = 22.5147473507269
x64 = 27.7507351067098
x65 = 65.4498469497874
x66 = 35.081117965086
x67 = 52.8834763354282
x68 = -85.3466004225227
x69 = -128.281700021583
x70 = -72.7802298081635
x70 = -72.7802298081635
The graph