Mister Exam

Other calculators

tan(x/3)=-(√3/3) 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]
            ___ 
   /x\   -\/ 3  
tan|-| = -------
   \3/      3   
$$\tan{\left(\frac{x}{3} \right)} = - \frac{\sqrt{3}}{3}$$
Detail solution
Given the equation
$$\tan{\left(\frac{x}{3} \right)} = - \frac{\sqrt{3}}{3}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{x}{3} = \pi n + \operatorname{atan}{\left(- \frac{\sqrt{3}}{3} \right)}$$
Or
$$\frac{x}{3} = \pi n - \frac{\pi}{6}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{1}{3}$$
we get the answer:
$$x_{1} = 3 \pi n - \frac{\pi}{2}$$
The graph
Rapid solution [src]
     -pi 
x1 = ----
      2  
$$x_{1} = - \frac{\pi}{2}$$
x1 = -pi/2
Sum and product of roots [src]
sum
-pi 
----
 2  
$$- \frac{\pi}{2}$$
=
-pi 
----
 2  
$$- \frac{\pi}{2}$$
product
-pi 
----
 2  
$$- \frac{\pi}{2}$$
=
-pi 
----
 2  
$$- \frac{\pi}{2}$$
-pi/2
Numerical answer [src]
x1 = 17.2787595947439
x2 = -10.9955742875643
x3 = -95.8185759344887
x4 = -48.6946861306418
x5 = 26.7035375555132
x6 = 36.1283155162826
x7 = 102.101761241668
x8 = 83.2522053201295
x9 = -76.9690200129499
x10 = -39.2699081698724
x11 = 45.553093477052
x12 = 64.4026493985908
x13 = -20.4203522483337
x14 = 7.85398163397448
x15 = -1.5707963267949
x16 = -67.5442420521806
x17 = -29.845130209103
x18 = -105.243353895258
x19 = -86.3937979737193
x20 = 73.8274273593601
x21 = -58.1194640914112
x22 = 92.6769832808989
x23 = 54.9778714378214
x23 = 54.9778714378214