Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 7x-15=4x-3(x-3)
-
Equation sin(pi*x)=0
- Equation 5x^2-125=0
-
Equation 1.2(5x-2)=8-(10.4-6x)
- Express {x} in terms of y where:
- -4*x+18*y=-14
- 8*x+7*y=-13
- 14*x-16*y=14
- -12*x+3*y=-9
- Graphing y =:
-
sin(0.5x)
- Integral of d{x}:
- sin(0.5x)
-
Identical expressions
- sin(zero .5x)=-sqrt3/ two
- sinus of (0.5x) equally minus square root of 3 divide by 2
- sinus of (zero .5x) equally minus square root of 3 divide by two
- sin(0.5x)=-√3/2
- sin0.5x=-sqrt3/2
- sin(0.5x)=-sqrt3 divide by 2
-
Similar expressions
- sin(x)+sqrt(((2-sqrt(3))/2)(cos(x)+1))=0
- cos(x)=-sqrt(3)/2
- 4sqrt((1-((sqrt(3))/2))/(6x+6))+pi/(6x+6)=1,5*sqrt(3)-2
- sin(0.5x)=+sqrt3/2
sin(0.5x)=-sqrt3/2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
___ /x\ -\/ 3 sin|-| = ------- \2/ 2
$$\sin{\left(\frac{x}{2} \right)} = \frac{\left(-1\right) \sqrt{3}}{2}$$
Detail solution
Given the equation
$$\sin{\left(\frac{x}{2} \right)} = \frac{\left(-1\right) \sqrt{3}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{x}{2} = 2 \pi n + \operatorname{asin}{\left(- \frac{\sqrt{3}}{2} \right)}$$
$$\frac{x}{2} = 2 \pi n - \operatorname{asin}{\left(- \frac{\sqrt{3}}{2} \right)} + \pi$$
Or
$$\frac{x}{2} = 2 \pi n - \frac{\pi}{3}$$
$$\frac{x}{2} = 2 \pi n + \frac{4 \pi}{3}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{1}{2}$$
we get the answer:
$$x_{1} = 4 \pi n - \frac{2 \pi}{3}$$
$$x_{2} = 4 \pi n + \frac{8 \pi}{3}$$
$$\sin{\left(\frac{x}{2} \right)} = \frac{\left(-1\right) \sqrt{3}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{x}{2} = 2 \pi n + \operatorname{asin}{\left(- \frac{\sqrt{3}}{2} \right)}$$
$$\frac{x}{2} = 2 \pi n - \operatorname{asin}{\left(- \frac{\sqrt{3}}{2} \right)} + \pi$$
Or
$$\frac{x}{2} = 2 \pi n - \frac{\pi}{3}$$
$$\frac{x}{2} = 2 \pi n + \frac{4 \pi}{3}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{1}{2}$$
we get the answer:
$$x_{1} = 4 \pi n - \frac{2 \pi}{3}$$
$$x_{2} = 4 \pi n + \frac{8 \pi}{3}$$
Rapid solution
[src]
-2*pi
x1 = -----
3
$$x_{1} = - \frac{2 \pi}{3}$$
8*pi
x2 = ----
3
$$x_{2} = \frac{8 \pi}{3}$$
x2 = 8*pi/3
Sum and product of roots
[src]
sum
2*pi 8*pi - ---- + ---- 3 3
$$- \frac{2 \pi}{3} + \frac{8 \pi}{3}$$
=
2*pi
$$2 \pi$$
product
-2*pi 8*pi -----*---- 3 3
$$- \frac{2 \pi}{3} \frac{8 \pi}{3}$$
=
2 -16*pi ------- 9
$$- \frac{16 \pi^{2}}{9}$$
-16*pi^2/9
Numerical answer
[src]
x1 = -92.1533845053006
x2 = -67.0206432765823
x3 = -90.0589894029074
x4 = 33.5103216382911
x5 = -102.625360017267
x6 = -54.4542726622231
x7 = 71.2094334813686
x8 = 73.3038285837618
x9 = -39.7935069454707
x10 = 98.4365698124802
x11 = -77.4926187885482
x12 = 1843.06769010601
x13 = 272.271363311115
x14 = 10.471975511966
x15 = -52.3598775598299
x16 = 58.6430628670095
x17 = 46.0766922526503
x18 = 96.342174710087
x19 = 20.943951023932
x20 = -41.8879020478639
x21 = -79.5870138909414
x22 = -27.2271363311115
x23 = -4.18879020478639
x24 = 85.870199198121
x25 = 23.0383461263252
x26 = 60.7374579694027
x27 = -44700.674670378
x28 = 8.37758040957278
x29 = -29.3215314335047
x30 = 48.1710873550435
x31 = 83.7758040957278
x32 = 35.6047167406843
x33 = -2.0943951023932
x34 = -16.7551608191456
x35 = -64.9262481741891
x36 = -366.519142918809
x37 = -203.15632493214
x38 = -14.6607657167524
x38 = -14.6607657167524