Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation sin0,5x=-(sqrt(3)/2)
- Equation x^4+5x^2-36=0
-
Equation 2sinx=5cosx
-
Equation 5(x+1)(x-3)=4x^2-8x
- Express {x} in terms of y where:
- 5*x-5*y=20
- 8*x-7*y=-13
- 15*x-15*y=16
- 9*x+18*y=6
- Graphing y =:
- sin0,5x
-
Identical expressions
- sin0,5x=-(sqrt(three)/ two)
- sinus of 0,5x equally minus ( square root of (3) divide by 2)
- sinus of 0,5x equally minus ( square root of (three) divide by two)
- sin0,5x=-(√(3)/2)
- sin0,5x=-sqrt3/2
- sin0,5x=-(sqrt(3) divide by 2)
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Similar expressions
- sin(3x)=-sqrt3/2
- 3sin(0,5x)+4cos(0,5x)=2
- sin2x=-(sqrt3/2)
- sin(x)=-sqrt(3)/2
- -4sin(0,5x)=0
- sin0,5x=+(sqrt(3)/2)
sin0,5x=-(sqrt(3)/2) equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
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-\/ 3
sin(0.5*x) = -------
2
$$\sin{\left(0.5 x \right)} = - \frac{\sqrt{3}}{2}$$
Detail solution
Given the equation
$$\sin{\left(0.5 x \right)} = - \frac{\sqrt{3}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$0.5 x = 2 \pi n + \operatorname{asin}{\left(- \frac{\sqrt{3}}{2} \right)}$$
$$0.5 x = 2 \pi n - \operatorname{asin}{\left(- \frac{\sqrt{3}}{2} \right)} + \pi$$
Or
$$0.5 x = 2 \pi n - \frac{\pi}{3}$$
$$0.5 x = 2 \pi n + \frac{4 \pi}{3}$$
, where n - is a integer
Divide both parts of the equation by
$$0.5$$
we get the answer:
$$x_{1} = 4 \pi n - 0.666666666666667 \pi$$
$$x_{2} = 4 \pi n + 2.66666666666667 \pi$$
$$\sin{\left(0.5 x \right)} = - \frac{\sqrt{3}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$0.5 x = 2 \pi n + \operatorname{asin}{\left(- \frac{\sqrt{3}}{2} \right)}$$
$$0.5 x = 2 \pi n - \operatorname{asin}{\left(- \frac{\sqrt{3}}{2} \right)} + \pi$$
Or
$$0.5 x = 2 \pi n - \frac{\pi}{3}$$
$$0.5 x = 2 \pi n + \frac{4 \pi}{3}$$
, where n - is a integer
Divide both parts of the equation by
$$0.5$$
we get the answer:
$$x_{1} = 4 \pi n - 0.666666666666667 \pi$$
$$x_{2} = 4 \pi n + 2.66666666666667 \pi$$
Sum and product of roots
[src]
sum
0 - 2.0943951023932 + 8.37758040957278
$$\left(-2.0943951023932 + 0\right) + 8.37758040957278$$
=
6.28318530717959
$$6.28318530717959$$
product
1*-2.0943951023932*8.37758040957278
$$1 \left(-2.0943951023932\right) 8.37758040957278$$
=
-17.5459633797144
$$-17.5459633797144$$
-17.5459633797144
Rapid solution
[src]
x1 = -2.0943951023932
$$x_{1} = -2.0943951023932$$
x2 = 8.37758040957278
$$x_{2} = 8.37758040957278$$
Numerical answer
[src]
x1 = 33.5103216382911
x2 = -16.7551608191456
x3 = 98.4365698124802
x4 = 48.1710873550435
x5 = 46.0766922526503
x6 = -92.1533845053006
x7 = 1843.06769010601
x8 = -27.2271363311115
x9 = 272.271363311115
x10 = 85.870199198121
x11 = -64.9262481741891
x12 = -54.4542726622231
x13 = 58.6430628670095
x14 = 73.3038285837618
x15 = -90.0589894029074
x16 = 71.2094334813686
x17 = -102.625360017267
x18 = -39.7935069454707
x19 = -77.4926187885482
x20 = -366.519142918809
x21 = 60.7374579694027
x22 = -41.8879020478639
x23 = 10.471975511966
x24 = 96.342174710087
x25 = 83.7758040957278
x26 = -79.5870138909414
x27 = -14.6607657167524
x28 = -2.0943951023932
x29 = 23.0383461263252
x30 = -29.3215314335047
x31 = -4.18879020478639
x32 = 8.37758040957278
x33 = -52.3598775598299
x34 = 20.943951023932
x35 = 35.6047167406843
x36 = -203.15632493214
x37 = -67.0206432765823
x38 = -44700.674670378
x38 = -44700.674670378
The graph