Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation cos(x)=-(1/2)
-
Equation 11x-9=4x+19
-
Equation x^4=(4*x-21)^2
-
Equation sqrt(x^2-x-1)-sqrt(x)=1
- Express {x} in terms of y where:
- 9*x+8*y=6
- -5*x+6*y=19
- 4*x+16*y=6
- -6*x+1*y=14
- Derivative of:
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cos(x)
- Graphing y =:
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cos(x)
- Integral of d{x}:
-
cos(x)
-
Identical expressions
- cos(x)=-(one / two)
- co sinus of e of (x) equally minus (1 divide by 2)
- co sinus of e of (x) equally minus (one divide by two)
- cosx=-1/2
- cos(x)=-(1 divide by 2)
-
Similar expressions
- 3sin^2x-7sinx×cosx+2cos^2x=0
- sin(5x)=-1/2
- (3)/(8y^3+1)-(1)/(2y+1)=(y+3)/(y^2-2y+1)
- (x-5)/2=2*(3x/7-1/2)/3
- cos(4pix/3)=-1/2
- cos(x)=+(1/2)
- cosx=-(1/2)
cos(x)=-(1/2) equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\cos{\left(x \right)} = - \frac{1}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{acos}{\left(- \frac{1}{2} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(- \frac{1}{2} \right)}$$
Or
$$x = \pi n + \frac{2 \pi}{3}$$
$$x = \pi n - \frac{\pi}{3}$$
, where n - is a integer
$$\cos{\left(x \right)} = - \frac{1}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{acos}{\left(- \frac{1}{2} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(- \frac{1}{2} \right)}$$
Or
$$x = \pi n + \frac{2 \pi}{3}$$
$$x = \pi n - \frac{\pi}{3}$$
, where n - is a integer
Rapid solution
[src]
2*pi
x1 = ----
3
$$x_{1} = \frac{2 \pi}{3}$$
4*pi
x2 = ----
3
$$x_{2} = \frac{4 \pi}{3}$$
x2 = 4*pi/3
Sum and product of roots
[src]
sum
2*pi 4*pi ---- + ---- 3 3
$$\frac{2 \pi}{3} + \frac{4 \pi}{3}$$
=
2*pi
$$2 \pi$$
product
2*pi 4*pi ----*---- 3 3
$$\frac{2 \pi}{3} \frac{4 \pi}{3}$$
=
2 8*pi ----- 9
$$\frac{8 \pi^{2}}{9}$$
8*pi^2/9
Numerical answer
[src]
x1 = -67.0206432765823
x2 = -33.5103216382911
x3 = 8.37758040957278
x4 = -41.8879020478639
x5 = -77.4926187885482
x6 = -79.5870138909414
x7 = 2.0943951023932
x8 = -35.6047167406843
x9 = 92.1533845053006
x10 = 23.0383461263252
x11 = -14.6607657167524
x12 = -23.0383461263252
x13 = -60.7374579694027
x14 = 27.2271363311115
x15 = -4.18879020478639
x16 = -20.943951023932
x17 = 41.8879020478639
x18 = -46.0766922526503
x19 = -90.0589894029074
x20 = 52.3598775598299
x21 = 67.0206432765823
x22 = 117.286125734019
x23 = 54.4542726622231
x24 = 73.3038285837618
x25 = 35.6047167406843
x26 = 90.0589894029074
x27 = 98.4365698124802
x28 = 630.412925820352
x29 = 60.7374579694027
x30 = -83.7758040957278
x31 = -1623.15620435473
x32 = -85.870199198121
x33 = 96.342174710087
x34 = 77.4926187885482
x35 = -71.2094334813686
x36 = 85.870199198121
x37 = 10.471975511966
x38 = 64.9262481741891
x39 = -27.2271363311115
x40 = -8.37758040957278
x41 = 16.7551608191456
x42 = -96.342174710087
x43 = -58.6430628670095
x44 = 29.3215314335047
x45 = 71.2094334813686
x46 = -98.4365698124802
x47 = 33.5103216382911
x48 = -29.3215314335047
x49 = -2.0943951023932
x50 = 83.7758040957278
x51 = -64.9262481741891
x52 = -52.3598775598299
x53 = 58.6430628670095
x54 = -92.1533845053006
x55 = 14.6607657167524
x56 = 79.5870138909414
x57 = 48.1710873550435
x58 = 46.0766922526503
x59 = -16.7551608191456
x60 = 39.7935069454707
x61 = 20.943951023932
x62 = 4.18879020478639
x63 = 416.784625376246
x64 = -73.3038285837618
x65 = -54.4542726622231
x66 = -48.1710873550435
x67 = -39.7935069454707
x68 = -10.471975511966
x68 = -10.471975511966
The graph