Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation cos(x)=2/3
- Equation x+y=3
-
Equation (x-11)^4=(x+3)^4
-
Equation 9-4x=3x-40
- Express {x} in terms of y where:
- 6*x+17*y=3
- -17*x+18*y=10
- 10*x-18*y=3
- 13*x-12*y=19
- Derivative of:
-
cos(x/2)
- Graphing y =:
- cos(x/2)
- Limit of the function:
-
cos(x/2)
-
Identical expressions
- cos(x/ two)= one
- co sinus of e of (x divide by 2) equally 1
- co sinus of e of (x divide by two) equally one
- cosx/2=1
- cos(x divide by 2)=1
-
Similar expressions
- sqrt(38)*cos(x/2+3pi/4)=sqrt(37-sin(3x))
- cos(x)x(cos(x)/2(sin(x)^3)^0.5)
- 2*cos(x)/2=0
- (1+2sin^2(x)+2sin(x)+2sin(x)*cos(x))/(2sin(x)*cos(x)-1)=1
cos(x/2)=1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\cos{\left(\frac{x}{2} \right)} = 1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{x}{2} = \pi n + \operatorname{acos}{\left(1 \right)}$$
$$\frac{x}{2} = \pi n - \pi + \operatorname{acos}{\left(1 \right)}$$
Or
$$\frac{x}{2} = \pi n$$
$$\frac{x}{2} = \pi n - \pi$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{1}{2}$$
we get the answer:
$$x_{1} = 2 \pi n$$
$$x_{2} = 2 \pi n - 2 \pi$$
$$\cos{\left(\frac{x}{2} \right)} = 1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{x}{2} = \pi n + \operatorname{acos}{\left(1 \right)}$$
$$\frac{x}{2} = \pi n - \pi + \operatorname{acos}{\left(1 \right)}$$
Or
$$\frac{x}{2} = \pi n$$
$$\frac{x}{2} = \pi n - \pi$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{1}{2}$$
we get the answer:
$$x_{1} = 2 \pi n$$
$$x_{2} = 2 \pi n - 2 \pi$$
Sum and product of roots
[src]
sum
4*pi
$$4 \pi$$
=
4*pi
$$4 \pi$$
product
0*4*pi
$$0 \cdot 4 \pi$$
=
0
$$0$$
0
Numerical answer
[src]
x1 = 12.566371289085
x2 = 25.1327427229237
x3 = 37.699112034073
x4 = 37.6991127786276
x5 = 8.5940846942539e-7
x6 = -37.6991126992556
x7 = 25.1327402133162
x8 = -339.292004463459
x9 = 87.964593548137
x10 = -2450.4422691113
x11 = 75.3982234996238
x12 = 100.530965273463
x13 = -50.2654829362526
x14 = 87.9645950596493
x15 = -62.831851347466
x16 = -9.20147750307351e-7
x17 = 12.5663724644809
x18 = -75.3982226734831
x19 = -87.9645950762365
x20 = -75.3982230244771
x21 = -75.3982238771266
x22 = 50.2654833855111
x23 = -25.1327409922366
x24 = -62.8318520510992
x25 = 37.6991112800661
x26 = -50.265481935943
x27 = -87.9645934511713
x28 = 50.2654816113039
x29 = 75.3982226607454
x30 = 62.8318527737309
x31 = 87.9645933670472
x32 = -12.5663711704395
x33 = 37.6991108423748
x34 = 25.1327422523855
x35 = 25.1327398318424
x36 = 62.8318520947719
x37 = -25.1327406696083
x38 = 25.1327416777796
x39 = -75.3982240789539
x40 = -62.8318526379222
x41 = -12.5663702980387
x42 = -25.1327422115415
x43 = -87.9645952061008
x44 = -7.64143136364703e-7
x45 = -50.2654834520414
x46 = -12.5663716390742
x47 = -25.1327415428233
x48 = 75.3982246787105
x49 = 12.5663716216992
x50 = 0.0
x51 = -50.2654831290744
x52 = -100.530964897478
x53 = 100.530964414577
x54 = 62.8318536450421
x55 = 62.8318531970184
x56 = 12.5663701654734
x57 = 50.2654832362872
x58 = -100.530963933814
x59 = 25.1327407976605
x60 = -62.8318540899534
x61 = -37.6991109019735
x62 = -50.2654815299205
x63 = 100.530964758156
x64 = 87.9645943359415
x65 = -12.5663696273954
x66 = -25.1327401961945
x67 = -37.6991125894353
x68 = -113.097333611656
x69 = -100.53096461474
x70 = -50.2654822841315
x71 = 75.3982242010893
x72 = -791.681347222187
x73 = 87.9645951697672
x74 = 37.6991123150382
x75 = 62.8318541035118
x76 = -12.5663706941362
x77 = 50.2654824463372
x78 = -62.8318542584121
x79 = 12.5663704404135
x80 = -37.6991118772906
x81 = 12.5663696903306
x82 = -75.398224618165
x83 = 100.530963999089
x84 = 75.3982240185352
x85 = 7.856665190876e-7
x86 = -62.8318535180004
x87 = 75.3982231443299
x88 = 50.2654816836948
x89 = 100.530964589585
x90 = -87.9645943585769
x91 = -87.9645934903961
x92 = -25.1327429452907
x93 = -37.6991110758133
x94 = 37.6991111844838
x94 = 37.6991111844838
The graph