Mister Exam
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Similar expressions
- 2*cos(pi/(2-x))=tan(x)
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2*cos(pi/2-x)=1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
/pi \
2*cos|-- - x| = 1
\2 /
$$2 \cos{\left(- x + \frac{\pi}{2} \right)} = 1$$
Detail solution
Given the equation
$$2 \cos{\left(- x + \frac{\pi}{2} \right)} = 1$$
- this is the simplest trigonometric equation
The equation is transformed to
$$\sin{\left(x \right)} = \frac{1}{2}$$
This equation is transformed to
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{1}{2} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{1}{2} \right)} + \pi$$
Or
$$x = 2 \pi n + \frac{\pi}{6}$$
$$x = 2 \pi n + \frac{5 \pi}{6}$$
, where n - is a integer
$$2 \cos{\left(- x + \frac{\pi}{2} \right)} = 1$$
- this is the simplest trigonometric equation
Divide both parts of the equation by 2
The equation is transformed to
$$\sin{\left(x \right)} = \frac{1}{2}$$
This equation is transformed to
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{1}{2} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{1}{2} \right)} + \pi$$
Or
$$x = 2 \pi n + \frac{\pi}{6}$$
$$x = 2 \pi n + \frac{5 \pi}{6}$$
, where n - is a integer
Sum and product of roots
[src]
sum
pi 5*pi -- + ---- 6 6
$$\frac{\pi}{6} + \frac{5 \pi}{6}$$
=
pi
$$\pi$$
product
pi 5*pi --*---- 6 6
$$\frac{\pi}{6} \frac{5 \pi}{6}$$
=
2 5*pi ----- 36
$$\frac{5 \pi^{2}}{36}$$
5*pi^2/36
Rapid solution
[src]
pi
x1 = --
6
$$x_{1} = \frac{\pi}{6}$$
5*pi
x2 = ----
6
$$x_{2} = \frac{5 \pi}{6}$$
x2 = 5*pi/6
Numerical answer
[src]
x1 = 71.733032256967
x2 = 78.0162175641465
x3 = -81.1578102177363
x4 = 69.6386371545737
x5 = 25.6563400043166
x6 = -79.0634151153431
x7 = -12.0427718387609
x8 = 82.2050077689329
x9 = -60.2138591938044
x10 = 101.054563690472
x11 = -24.60914245312
x12 = 138.753675533549
x13 = -53.9306738866248
x14 = -97.9129710368819
x15 = -72.7802298081635
x16 = -18.3259571459405
x17 = -43.4586983746588
x18 = 90.5825881785057
x19 = 6.80678408277789
x20 = 17438.4572213013
x21 = 84.2994028713261
x22 = 59.1666616426078
x23 = 63.3554518473942
x24 = 0.523598775598299
x25 = -56.025068989018
x26 = -16.2315620435473
x27 = 38.2227106186758
x28 = -22.5147473507269
x29 = 31.9395253114962
x30 = -37.1755130674792
x31 = 134.564885328763
x32 = -30.8923277602996
x33 = 40.317105721069
x34 = 88.4881930761125
x35 = 50.789081233035
x36 = 13.0899693899575
x37 = -62.3082542961976
x38 = -28.7979326579064
x39 = -41.3643032722656
x40 = -74.8746249105567
x41 = 44.5058959258554
x42 = -85.3466004225227
x43 = -47.6474885794452
x44 = 94.7713783832921
x45 = -9.94837673636768
x46 = -91.6297857297023
x47 = 46.6002910282486
x48 = -3.66519142918809
x49 = 75.9218224617533
x50 = 96.8657734856853
x51 = 34.0339204138894
x52 = -5.75958653158129
x53 = -100.007366139275
x54 = -66.497044500984
x55 = -2650.98060085419
x56 = -627.79493194236
x57 = -49.7418836818384
x58 = -35.081117965086
x59 = 52.8834763354282
x60 = 2.61799387799149
x61 = 19.3731546971371
x62 = -87.4409955249159
x63 = 65.4498469497874
x64 = 8.90117918517108
x65 = 21.4675497995303
x66 = 57.0722665402146
x67 = -93.7241808320955
x68 = -4454.25478401473
x69 = 27.7507351067098
x70 = 15.1843644923507
x71 = -68.5914396033772
x71 = -68.5914396033772