Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 3(x+3)=2x+5
-
Equation x^2=8
-
Equation (x-3)*(x+2)=0
-
Equation 1/(x+6)=2
- Express {x} in terms of y where:
- 2*x+13*y=19
- -17*x+18*y=10
- 7*x-1*y=-7
- 10*x-18*y=3
- Derivative of:
-
-cos(x)
- Integral of d{x}:
-
-cos(x)
- Limit of the function:
-
-cos(x)
-
Identical expressions
- -cos(x)=-(√ three / two)
- minus co sinus of e of (x) equally minus (√3 divide by 2)
- minus co sinus of e of (x) equally minus (√ three divide by two)
- -cosx=-√3/2
- -cos(x)=-(√3 divide by 2)
-
Similar expressions
- -cosx/3-√3/2/3=0
- -cos(x)=+(√3/2)
- cos(x)=-(√3/2)
- sin(2x)=2sinx-cosx+1
- cos(-2x)=-√3/2
- sin(-2x-(p/6))=-√3/2
- 2sin2-cosx=sqrt3*sinx
- -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
$$- \cos{\left(x \right)} = - \frac{\sqrt{3}}{2}$$
Detail solution
Given the equation
$$- \cos{\left(x \right)} = - \frac{\sqrt{3}}{2}$$
- this is the simplest trigonometric equation
The equation is transformed to
$$\cos{\left(x \right)} = \frac{\sqrt{3}}{2}$$
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
$$x = \pi n + \frac{\pi}{6}$$
$$x = \pi n - \frac{5 \pi}{6}$$
, where n - is a integer
$$- \cos{\left(x \right)} = - \frac{\sqrt{3}}{2}$$
- this is the simplest trigonometric equation
Divide both parts of the equation by -1
The equation is transformed to
$$\cos{\left(x \right)} = \frac{\sqrt{3}}{2}$$
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
$$x = \pi n + \frac{\pi}{6}$$
$$x = \pi n - \frac{5 \pi}{6}$$
, where n - is a integer
Sum and product of roots
[src]
sum
pi 11*pi -- + ----- 6 6
$$\frac{\pi}{6} + \frac{11 \pi}{6}$$
=
2*pi
$$2 \pi$$
product
pi 11*pi --*----- 6 6
$$\frac{\pi}{6} \frac{11 \pi}{6}$$
=
2 11*pi ------ 36
$$\frac{11 \pi^{2}}{36}$$
11*pi^2/36
Rapid solution
[src]
pi
x1 = --
6
$$x_{1} = \frac{\pi}{6}$$
11*pi
x2 = -----
6
$$x_{2} = \frac{11 \pi}{6}$$
x2 = 11*pi/6
Numerical answer
[src]
x1 = 62.3082542961976
x2 = -93.7241808320955
x3 = 69.6386371545737
x4 = -25.6563400043166
x5 = -94.7713783832921
x6 = 57.0722665402146
x7 = -30.8923277602996
x8 = -24.60914245312
x9 = 5.75958653158129
x10 = 100.007366139275
x11 = -74.8746249105567
x12 = 87.4409955249159
x13 = 63.3554518473942
x14 = -69.6386371545737
x15 = 24.60914245312
x16 = 194.255145746969
x17 = -31.9395253114962
x18 = -43.4586983746588
x19 = -37.1755130674792
x20 = 30.8923277602996
x21 = -75.9218224617533
x22 = 0.523598775598299
x23 = -82.2050077689329
x24 = 38.2227106186758
x25 = -68.5914396033772
x26 = 44.5058959258554
x27 = 43.4586983746588
x28 = 94.7713783832921
x29 = 37.1755130674792
x30 = 93.7241808320955
x31 = 68.5914396033772
x32 = 18.3259571459405
x33 = -0.523598775598299
x34 = 50.789081233035
x35 = -50.789081233035
x36 = 74.8746249105567
x37 = -87.4409955249159
x38 = -5.75958653158129
x39 = -56.025068989018
x40 = 19.3731546971371
x41 = 13.0899693899575
x42 = -57.0722665402146
x43 = -12.0427718387609
x44 = 6.80678408277789
x45 = -44.5058959258554
x46 = -81.1578102177363
x47 = -13.0899693899575
x48 = 88.4881930761125
x49 = -88.4881930761125
x50 = -18.3259571459405
x51 = 31.9395253114962
x52 = 82.2050077689329
x53 = -101.054563690472
x54 = 56.025068989018
x55 = 75.9218224617533
x56 = -38.2227106186758
x57 = 49.7418836818384
x58 = -6.80678408277789
x59 = 81.1578102177363
x60 = -100.007366139275
x61 = -62.3082542961976
x62 = 1168.1488683598
x63 = -49.7418836818384
x64 = 12.0427718387609
x65 = -19.3731546971371
x66 = 25.6563400043166
x67 = -63.3554518473942
x67 = -63.3554518473942