Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 1-7*(4+2*x)=-9-4*x
-
Equation sin(x)=2
-
Equation -x-2+3(x-3)=3(4-x)-3
-
Equation 4x=24+x
- Express {x} in terms of y where:
- -6*x-2*y=-10
- 18*x+14*y=-11
- -8*x-12*y=15
- sin(xy)+cos(xy)=tg(x+y)
- Limit of the function:
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tan(x/3)
-
Identical expressions
- tan(x/ three)=-(√ three / three)
- tangent of (x divide by 3) equally minus (√3 divide by 3)
- tangent of (x divide by three) equally minus (√ three divide by three)
- tanx/3=-√3/3
- tan(x divide by 3)=-(√3 divide by 3)
-
Similar expressions
- tg3x=-√3/3
- tan(x/3+pi/6)=-1
- tan(x/3)=+(√3/3)
- (tg(pi*(x+10)/3))=-√3/3
- tg(pi(x+10)/3)=-√3/3
- tan(x/2)=-√3/3
- tan(x)/3+1=0
tan(x/3)=-(√3/3) equation
The teacher will be very surprised to see your correct solution 😉
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:
$$x_{1} = 3 \pi n - \frac{\pi}{2}$$
$$\tan{\left(\frac{x}{3} \right)} = - \frac{\sqrt{3}}{3}$$
- 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:
$$x_{1} = 3 \pi n - \frac{\pi}{2}$$
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