Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 0,2x+2,7=1,4-1,1x
-
Equation -x^2+6*x+16=0
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Equation sin(x/3)=1/2
- Equation x^4-50*x^2+49=0
- Express {x} in terms of y where:
- 12*x-20*y=10
- -1*x+6*y=-20
- -11*x+10*y=-3
- 7*x-6*y=-2
- Graphing y =:
- sin(x/3)
- Integral of d{x}:
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sin(x/3)
-
1/2
- Limit of the function:
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sin(x/3)
- Sum of series:
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1/2
- Derivative of:
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1/2
-
Identical expressions
- sin(x/ three)= one / two
- sinus of (x divide by 3) equally 1 divide by 2
- sinus of (x divide by three) equally one divide by two
- sinx/3=1/2
- sin(x divide by 3)=1 divide by 2
-
Similar expressions
- (x-1)/(2x+3)-(2x-1)/(3-2x)=0
- -1/2*sin(x/3-пи/18)-2,5=0
sin(x/3)=1/2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sin{\left(\frac{x}{3} \right)} = \frac{1}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{x}{3} = 2 \pi n + \operatorname{asin}{\left(\frac{1}{2} \right)}$$
$$\frac{x}{3} = 2 \pi n - \operatorname{asin}{\left(\frac{1}{2} \right)} + \pi$$
Or
$$\frac{x}{3} = 2 \pi n + \frac{\pi}{6}$$
$$\frac{x}{3} = 2 \pi n + \frac{5 \pi}{6}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{1}{3}$$
we get the answer:
$$x_{1} = 6 \pi n + \frac{\pi}{2}$$
$$x_{2} = 6 \pi n + \frac{5 \pi}{2}$$
$$\sin{\left(\frac{x}{3} \right)} = \frac{1}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{x}{3} = 2 \pi n + \operatorname{asin}{\left(\frac{1}{2} \right)}$$
$$\frac{x}{3} = 2 \pi n - \operatorname{asin}{\left(\frac{1}{2} \right)} + \pi$$
Or
$$\frac{x}{3} = 2 \pi n + \frac{\pi}{6}$$
$$\frac{x}{3} = 2 \pi n + \frac{5 \pi}{6}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{1}{3}$$
we get the answer:
$$x_{1} = 6 \pi n + \frac{\pi}{2}$$
$$x_{2} = 6 \pi n + \frac{5 \pi}{2}$$
Sum and product of roots
[src]
sum
pi 5*pi -- + ---- 2 2
$$\frac{\pi}{2} + \frac{5 \pi}{2}$$
=
3*pi
$$3 \pi$$
product
pi 5*pi --*---- 2 2
$$\frac{\pi}{2} \frac{5 \pi}{2}$$
=
2 5*pi ----- 4
$$\frac{5 \pi^{2}}{4}$$
5*pi^2/4
Rapid solution
[src]
pi
x1 = --
2
$$x_{1} = \frac{\pi}{2}$$
5*pi
x2 = ----
2
$$x_{2} = \frac{5 \pi}{2}$$
x2 = 5*pi/2
Numerical answer
[src]
x1 = 102.101761241668
x2 = -17.2787595947439
x3 = 95.8185759344887
x4 = 3658.38464510531
x5 = -519.933584169111
x6 = 76.9690200129499
x7 = -36.1283155162826
x8 = -92.6769832808989
x9 = 1.5707963267949
x10 = 64.4026493985908
x11 = 20.4203522483337
x12 = -3837.45542635993
x13 = 2452.01306612683
x14 = 26.7035375555132
x15 = -29.845130209103
x16 = -10.9955742875643
x17 = -237.190245346029
x18 = 83.2522053201295
x19 = -180.641577581413
x20 = -73.8274273593601
x21 = 45.553093477052
x22 = -48.6946861306418
x23 = -1518.96004801067
x24 = 58.1194640914112
x25 = 39.2699081698724
x26 = -54.9778714378214
x27 = -86.3937979737193
x28 = 114.668131856027
x29 = 7.85398163397448
x30 = -67.5442420521806
x30 = -67.5442420521806
The graph