Mister Exam
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How to use it?
- Equation:
-
Equation 4(x-6)=x-9
-
Equation sin(x/2)=1
-
Equation x*(x^2+8*x+16)=5*(x+4)
- Equation x^4-15*x^2-16=0
- Express {x} in terms of y where:
- -6*x-10*y=19
- 9*x+17*y=13
- 20*x+18*y=-9
- -17*x+2*y=-4
- Derivative of:
-
sin(x/2)
- Graphing y =:
- sin(x/2)
- Integral of d{x}:
-
sin(x/2)
-
Identical expressions
- sin(x/ two)= one
- sinus of (x divide by 2) equally 1
- sinus of (x divide by two) equally one
- sinx/2=1
- sin(x divide by 2)=1
-
Similar expressions
- sin(x)*cos(x)+sqrt(3)*sin(x)/2=0
- 2sin^2(x)-sqrt(3)sin(x)/2cos(x)+1=0
sin(x/2)=1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sin{\left(\frac{x}{2} \right)} = 1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{x}{2} = 2 \pi n + \operatorname{asin}{\left(1 \right)}$$
$$\frac{x}{2} = 2 \pi n - \operatorname{asin}{\left(1 \right)} + \pi$$
Or
$$\frac{x}{2} = 2 \pi n + \frac{\pi}{2}$$
$$\frac{x}{2} = 2 \pi n + \frac{\pi}{2}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{1}{2}$$
we get the answer:
$$x_{1} = 4 \pi n + \pi$$
$$x_{2} = 4 \pi n + \pi$$
$$\sin{\left(\frac{x}{2} \right)} = 1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{x}{2} = 2 \pi n + \operatorname{asin}{\left(1 \right)}$$
$$\frac{x}{2} = 2 \pi n - \operatorname{asin}{\left(1 \right)} + \pi$$
Or
$$\frac{x}{2} = 2 \pi n + \frac{\pi}{2}$$
$$\frac{x}{2} = 2 \pi n + \frac{\pi}{2}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{1}{2}$$
we get the answer:
$$x_{1} = 4 \pi n + \pi$$
$$x_{2} = 4 \pi n + \pi$$
Numerical answer
[src]
x1 = 40.8407041945824
x2 = -84.8230026657071
x3 = 53.40707409148
x4 = 40.8407055286336
x5 = 15.707964515786
x6 = -9.42477813898924
x7 = -9.42477728929078
x8 = -59.6902612768606
x9 = 28.2743338651742
x10 = 16741.5472539237
x11 = 78.5398173426089
x12 = 78.5398170241526
x13 = 28.2743330336433
x14 = 91.1061874144797
x15 = 91.1061859410303
x16 = -72.2566304993376
x17 = 53.4070749521362
x18 = -34.5575202139462
x19 = 15.7079637526952
x20 = -72.2566334561862
x21 = -47.123889537864
x22 = 3.14159367655067
x23 = 28.2743346582797
x24 = 3.14159131070869
x25 = 78.539815851887
x26 = 91.1061853899956
x27 = 28.2743348137489
x28 = 53.4070761022138
x29 = -21.9911494917557
x30 = 40.840705066392
x31 = 40.8407056713041
x32 = -59.690260457841
x33 = -84.8230020968984
x34 = -9.42477695202933
x35 = -34.5575192441112
x36 = 15.7079632663563
x37 = 53.4070754394033
x38 = 40.840704648726
x39 = 65.9734457530019
x40 = -47.1238918185856
x41 = 78.5398154218754
x42 = 53.4070740857414
x43 = 65.9734447951365
x44 = 14944.5562553885
x45 = -59.6902596538675
x46 = 40.8407035181637
x47 = 15.7079622686986
x48 = 15.7079626060796
x49 = -72.2566317074393
x50 = 53.4070745656255
x51 = -59.6902611573573
x52 = 65.9734449700497
x53 = -34.5575188772018
x54 = -84.8230027834212
x55 = -21.9911493421841
x56 = 91.106187979742
x57 = 15.7079634545545
x58 = -34.5575197491116
x59 = -47.1238901219454
x60 = -59.6902594740223
x61 = -21.9911477182159
x62 = 91.1061865344779
x63 = -21.9911485864393
x64 = -47.1238892482917
x65 = 65.9734465921985
x66 = -47.1238907880697
x67 = 3.14159163746103
x68 = 78.5398162375612
x69 = -9.42477888681821
x70 = 103.672556563684
x71 = 91.1061882841015
x72 = 3.14159309886503
x73 = -9.4247756652542
x74 = -34.5575182039711
x75 = -9.42477839608986
x76 = -72.2566308637416
x77 = -21.9911477831607
x78 = -47.1238887712007
x79 = 3.14159420425446
x80 = -97.389371602892
x81 = -72.2566301070981
x82 = 28.2743331152018
x83 = -72.2566320255231
x84 = -97.3893712473886
x85 = 3.14159221873501
x86 = 78.5398161786998
x87 = -84.8230012168657
x88 = 65.973446491358
x89 = 15.7079642015151
x90 = -84.8229998635885
x91 = -97.389373195247
x92 = -97.3893724564835
x93 = -84.8230006270304
x93 = -84.8230006270304
The graph