Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 1-5*x=-6*x+8
-
Equation 8*x-3*(2*x+1)=2*x+4
-
Equation 3^x+4^x=5^x
-
Equation x^4=(3*x-4)^2
- Express {x} in terms of y where:
- 7*x+19*y=12
- -9*x-4*y=-20
- 12*x-14*y=20
- -18*x+8*y=-2
- Derivative of:
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ctg(x)
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1/2
- Integral of d{x}:
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ctg(x)
-
1/2
- Graphing y =:
- ctg(x)
- Sum of series:
-
1/2
-
Identical expressions
- ctg(x)= one / two
- ctg(x) equally 1 divide by 2
- ctg(x) equally one divide by two
- ctgx=1/2
- ctg(x)=1 divide by 2
-
Similar expressions
- arctg(x/3)=x/4
ctg(x)=1/2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\cot{\left(x \right)} = \frac{1}{2}$$
transform
$$\cot{\left(x \right)} - \frac{1}{2} = 0$$
$$\cot{\left(x \right)} - \frac{1}{2} = 0$$
Do replacement
$$w = \cot{\left(x \right)}$$
Move free summands (without w)
from left part to right part, we given:
$$w = \frac{1}{2}$$
We get the answer: w = 1/2
do backward replacement
$$\cot{\left(x \right)} = w$$
substitute w:
$$\cot{\left(x \right)} = \frac{1}{2}$$
transform
$$\cot{\left(x \right)} - \frac{1}{2} = 0$$
$$\cot{\left(x \right)} - \frac{1}{2} = 0$$
Do replacement
$$w = \cot{\left(x \right)}$$
Move free summands (without w)
from left part to right part, we given:
$$w = \frac{1}{2}$$
We get the answer: w = 1/2
do backward replacement
$$\cot{\left(x \right)} = w$$
substitute w:
Sum and product of roots
[src]
sum
acot(1/2)
$$\operatorname{acot}{\left(\frac{1}{2} \right)}$$
=
acot(1/2)
$$\operatorname{acot}{\left(\frac{1}{2} \right)}$$
product
acot(1/2)
$$\operatorname{acot}{\left(\frac{1}{2} \right)}$$
=
acot(1/2)
$$\operatorname{acot}{\left(\frac{1}{2} \right)}$$
acot(1/2)
Rapid solution
[src]
x1 = acot(1/2)
$$x_{1} = \operatorname{acot}{\left(\frac{1}{2} \right)}$$
x1 = acot(1/2)
Numerical answer
[src]
x1 = 1.10714871779409
x2 = 67.0805944431797
x3 = 82.7885577111287
x4 = -68.0078896611814
x5 = 19.9567046393328
x6 = -5.1760365893855
x7 = 98.4965209790777
x8 = -14.6008145501549
x9 = -17.7424072037447
x10 = -30.3087778181038
x11 = -24.0255925109243
x12 = -64.8662970075916
x13 = 4.24874137138388
x14 = -42.875148432463
x15 = 60.7974091360002
x16 = -11.4592218965651
x17 = 16.8151119857431
x18 = 51.3726311752308
x19 = -89.9990382363099
x20 = -74.2910749683609
x21 = -49.1583337396426
x22 = -27.167185164514
x23 = 85.9301503647185
x24 = -46.0167410860528
x25 = -83.7158529291303
x26 = 79.6469650575389
x27 = 26.2398899465124
x28 = 73.3637797503593
x29 = 92.2133356718981
x30 = 57.6558164824104
x31 = 54.5142238288206
x32 = -99.4238161970793
x33 = -20.8839998573345
x34 = 13.6735193321533
x35 = -39.7335557788732
x36 = 38.8062605608716
x37 = -58.583111700412
x38 = 10.5319266785635
x39 = 95.3549283254879
x40 = 41.9478532144614
x41 = 32.523075253692
x42 = -96.2822235434895
x43 = 70.2221870967695
x44 = 29.3814826001022
x45 = 63.93900178959
x46 = 48.231038521641
x47 = -61.7247043540018
x48 = 23.0982972929226
x49 = -2.0344439357957
x50 = -71.1494823147711
x51 = -77.4326676219507
x52 = -93.1406308898997
x53 = 89.0717430183083
x54 = -55.4415190468222
x55 = -80.5742602755405
x56 = -36.5919631252834
x57 = -33.4503704716936
x58 = -8.31762924297529
x59 = -52.2999263932324
x60 = -86.8574455827201
x61 = 45.0894458680512
x62 = 35.6646679072818
x63 = 7.39033402497368
x64 = 76.5053724039491
x64 = 76.5053724039491