Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 17x-8=20x+7
-
Equation 2*x^2+6*x+9=
-
Equation (x-2)^2=(x-9)^2
-
Equation -x=8
- Express {x} in terms of y where:
- 17*x+20*y=-12
- 17*x+16*y=7
- -5*x+6*y=19
- 18*x-14*y=-12
- Integral of d{x}:
-
tan(x/2)
- Graphing y =:
-
tan(x/2)
- Limit of the function:
-
tan(x/2)
-
Identical expressions
- tan(x/ two)=-√ three / three
- tangent of (x divide by 2) equally minus √3 divide by 3
- tangent of (x divide by two) equally minus √ three divide by three
- tanx/2=-√3/3
- tan(x divide by 2)=-√3 divide by 3
-
Similar expressions
- tan(x/2-pi/5)=1
- tan(x/2)=+√3/3
tan(x/2)=-√3/3 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
___ /x\ -\/ 3 tan|-| = ------- \2/ 3
$$\tan{\left(\frac{x}{2} \right)} = \frac{\left(-1\right) \sqrt{3}}{3}$$
Detail solution
Given the equation
$$\tan{\left(\frac{x}{2} \right)} = \frac{\left(-1\right) \sqrt{3}}{3}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{x}{2} = \pi n + \operatorname{atan}{\left(- \frac{\sqrt{3}}{3} \right)}$$
Or
$$\frac{x}{2} = \pi n - \frac{\pi}{6}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{1}{2}$$
we get the answer:
$$x_{1} = 2 \pi n - \frac{\pi}{3}$$
$$\tan{\left(\frac{x}{2} \right)} = \frac{\left(-1\right) \sqrt{3}}{3}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{x}{2} = \pi n + \operatorname{atan}{\left(- \frac{\sqrt{3}}{3} \right)}$$
Or
$$\frac{x}{2} = \pi n - \frac{\pi}{6}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{1}{2}$$
we get the answer:
$$x_{1} = 2 \pi n - \frac{\pi}{3}$$
Sum and product of roots
[src]
sum
-pi ---- 3
$$- \frac{\pi}{3}$$
=
-pi ---- 3
$$- \frac{\pi}{3}$$
product
-pi ---- 3
$$- \frac{\pi}{3}$$
=
-pi ---- 3
$$- \frac{\pi}{3}$$
-pi/3
Numerical answer
[src]
x1 = 30.3687289847013
x2 = 36.6519142918809
x3 = 55.5014702134197
x4 = 74.3510261349584
x5 = -51.3126800086333
x6 = -45.0294947014537
x7 = 99.4837673636768
x8 = -19.8967534727354
x9 = -13.6135681655558
x10 = 61.7846555205993
x11 = 11.5191730631626
x12 = 93.2005820564972
x13 = 80.634211442138
x14 = -38.7463093942741
x15 = -76.4454212373516
x16 = -95.2949771588904
x17 = -57.5958653158129
x18 = 24.0855436775217
x19 = 5.23598775598299
x20 = -32.4631240870945
x21 = -63.8790506229925
x22 = -26.1799387799149
x23 = -70.162235930172
x24 = -101.57816246607
x25 = 17.8023583703422
x26 = -7.33038285837618
x27 = 49.2182849062401
x28 = -89.0117918517108
x29 = -1.0471975511966
x30 = 68.0678408277789
x31 = 86.9173967493176
x32 = -82.7286065445312
x33 = 42.9350995990605
x33 = 42.9350995990605