Mister Exam

Other calculators

3tg(x)=2cos(x) equation

The teacher will be very surprised to see your correct solution 😉

v

Numerical solution:

Do search numerical solution at [, ]

The solution

You have entered [src] 
3*tan(x) = 2*cos(x)
$$3 \tan{\left(x \right)} = 2 \cos{\left(x \right)}$$
Simplify
The graph
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
     pi
x1 = --
     6
$$x_{1} = \frac{\pi}{6}$$ 
     5*pi
x2 = ----
      6
$$x_{2} = \frac{5 \pi}{6}$$ 
       pi        /      ___\
x3 = - -- - I*log\2 - \/ 3 /
       2
$$x_{3} = - \frac{\pi}{2} - i \log{\left(2 - \sqrt{3} \right)}$$ 
       pi        /      ___\
x4 = - -- - I*log\2 + \/ 3 /
       2
$$x_{4} = - \frac{\pi}{2} - i \log{\left(\sqrt{3} + 2 \right)}$$ 
x4 = -pi/2 - i*log(sqrt(3) + 2)
Sum and product of roots [src] 
sum
pi   5*pi     pi        /      ___\     pi        /      ___\
-- + ---- + - -- - I*log\2 - \/ 3 / + - -- - I*log\2 + \/ 3 /
6     6       2                         2
$$\left(- \frac{\pi}{2} - i \log{\left(\sqrt{3} + 2 \right)}\right) + \left(\left(\frac{\pi}{6} + \frac{5 \pi}{6}\right) + \left(- \frac{\pi}{2} - i \log{\left(2 - \sqrt{3} \right)}\right)\right)$$ 
=
       /      ___\        /      ___\
- I*log\2 + \/ 3 / - I*log\2 - \/ 3 /
$$- i \log{\left(\sqrt{3} + 2 \right)} - i \log{\left(2 - \sqrt{3} \right)}$$ 
product
pi 5*pi /  pi        /      ___\\ /  pi        /      ___\\
--*----*|- -- - I*log\2 - \/ 3 /|*|- -- - I*log\2 + \/ 3 /|
6   6   \  2                    / \  2                    /
$$\frac{\pi}{6} \frac{5 \pi}{6} \left(- \frac{\pi}{2} - i \log{\left(2 - \sqrt{3} \right)}\right) \left(- \frac{\pi}{2} - i \log{\left(\sqrt{3} + 2 \right)}\right)$$ 
=
    2 /            /      ___\\ /            /      ___\\
5*pi *\pi + 2*I*log\2 + \/ 3 //*\pi + 2*I*log\2 - \/ 3 //
---------------------------------------------------------
                           144
$$\frac{5 \pi^{2} \left(\pi + 2 i \log{\left(2 - \sqrt{3} \right)}\right) \left(\pi + 2 i \log{\left(\sqrt{3} + 2 \right)}\right)}{144}$$ 
5*pi^2*(pi + 2*i*log(2 + sqrt(3)))*(pi + 2*i*log(2 - sqrt(3)))/144
Numerical answer [src] 
x1 = 25.6563400043166
x2 = -62.3082542961976
x3 = -74.8746249105567
x4 = -81.1578102177363
x5 = -53.9306738866248
x6 = -49.7418836818384
x7 = 15.1843644923507
x8 = -97.9129710368819
x9 = 82.2050077689329
x10 = -5.75958653158129
x11 = -100.007366139275
x12 = -22.5147473507269
x13 = -37.1755130674792
x14 = -66.497044500984
x15 = 88.4881930761125
x16 = -3.66519142918809
x17 = 31.9395253114962
x18 = -72.7802298081635
x19 = 78.0162175641465
x20 = 19.3731546971371
x21 = -87.4409955249159
x22 = 50.789081233035
x23 = -24.60914245312
x24 = 40.317105721069
x25 = -30.8923277602996
x26 = 84.2994028713261
x27 = -79.0634151153431
x28 = 96.8657734856853
x29 = 101.054563690472
x30 = 59.1666616426078
x31 = 27.7507351067098
x32 = -16.2315620435473
x33 = -85.3466004225227
x34 = 52.8834763354282
x35 = 63.3554518473942
x36 = -47.6474885794452
x37 = 90.5825881785057
x38 = 34.0339204138894
x39 = 57.0722665402146
x40 = 8.90117918517108
x41 = 21.4675497995303
x42 = 44.5058959258554
x43 = 13.0899693899575
x44 = -68.5914396033772
x45 = 65.4498469497874
x46 = -35.081117965086
x47 = 46.6002910282486
x48 = 71.733032256967
x49 = 0.523598775598299
x50 = -41.3643032722656
x51 = -12.0427718387609
x52 = 6.80678408277789
x53 = 38.2227106186758
x54 = -60.2138591938044
x55 = -43.4586983746588
x56 = -93.7241808320955
x57 = 2.61799387799149
x58 = 69.6386371545737
x59 = -18.3259571459405
x60 = -28.7979326579064
x61 = 75.9218224617533
x62 = -56.025068989018
x63 = -91.6297857297023
x64 = -9.94837673636768
x65 = 94.7713783832921
x65 = 94.7713783832921
    © Mister Exam – Calculator