Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation x^2+3x+2=0
- Equation x+y=5
-
Equation sin(x)=3
-
Equation x^2-11*x+30=0
- Express {x} in terms of y where:
- 6*x+17*y=-11
- -13*x+7*y=-15
- -14*x-8*y=20
- 9*x+14*y=-10
- Limit of the function:
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sin(pi*x/3)
- Sum of series:
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1/2
- Derivative of:
-
1/2
- Integral of d{x}:
-
1/2
-
Identical expressions
- sin(pi*x/ three)= one / two
- sinus of ( Pi multiply by x divide by 3) equally 1 divide by 2
- sinus of ( Pi multiply by x divide by three) equally one divide by two
- sin(pix/3)=1/2
- sinpix/3=1/2
- sin(pi*x divide by 3)=1 divide by 2
-
Similar expressions
- 1/(2*1,0038*1000)*((1,848/3600*287)/(2544,7*10^(-9)*55,688*10^(3)))^(2)*x^(2)+x-295,15=0
- sin(pi*x)/3=-1/2
- sin3x-sin7x+cos4x+sinx=(1)/(2)
sin(pi*x/3)=1/2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
/pi*x\ sin|----| = 1/2 \ 3 /
$$\sin{\left(\frac{\pi x}{3} \right)} = \frac{1}{2}$$
Detail solution
Given the equation
$$\sin{\left(\frac{\pi x}{3} \right)} = \frac{1}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{\pi x}{3} = 2 \pi n + \operatorname{asin}{\left(\frac{1}{2} \right)}$$
$$\frac{\pi x}{3} = 2 \pi n - \operatorname{asin}{\left(\frac{1}{2} \right)} + \pi$$
Or
$$\frac{\pi x}{3} = 2 \pi n + \frac{\pi}{6}$$
$$\frac{\pi x}{3} = 2 \pi n + \frac{5 \pi}{6}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{\pi}{3}$$
we get the answer:
$$x_{1} = \frac{3 \left(2 \pi n + \frac{\pi}{6}\right)}{\pi}$$
$$x_{2} = \frac{3 \left(2 \pi n + \frac{5 \pi}{6}\right)}{\pi}$$
$$\sin{\left(\frac{\pi x}{3} \right)} = \frac{1}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{\pi x}{3} = 2 \pi n + \operatorname{asin}{\left(\frac{1}{2} \right)}$$
$$\frac{\pi x}{3} = 2 \pi n - \operatorname{asin}{\left(\frac{1}{2} \right)} + \pi$$
Or
$$\frac{\pi x}{3} = 2 \pi n + \frac{\pi}{6}$$
$$\frac{\pi x}{3} = 2 \pi n + \frac{5 \pi}{6}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{\pi}{3}$$
we get the answer:
$$x_{1} = \frac{3 \left(2 \pi n + \frac{\pi}{6}\right)}{\pi}$$
$$x_{2} = \frac{3 \left(2 \pi n + \frac{5 \pi}{6}\right)}{\pi}$$
Sum and product of roots
[src]
sum
1/2 + 5/2
$$\frac{1}{2} + \frac{5}{2}$$
=
3
$$3$$
product
5 --- 2*2
$$\frac{5}{2 \cdot 2}$$
=
5/4
$$\frac{5}{4}$$
5/4
Numerical answer
[src]
x1 = 98.5
x2 = 8.5
x3 = 56.5
x4 = -65.5
x5 = 6.5
x6 = -71.5
x7 = -39.5
x8 = 36.5
x9 = 2.5
x10 = -35.5
x11 = -83.5
x12 = 68.5
x13 = 30.5
x14 = -53.5
x15 = 74.5
x16 = 60.5
x17 = 12.5
x18 = 26.5
x19 = 44.5
x20 = -17.5
x21 = 42.5
x22 = 72.5
x23 = 78.5
x24 = -47.5
x25 = 96.5
x26 = -41.5
x27 = -101.5
x28 = 50.5
x29 = 20.5
x30 = 92.5
x31 = -9.5
x32 = -15.5
x33 = -63.5
x34 = -21.5
x35 = -89.5
x36 = -69.5
x37 = -99.5
x38 = -27.5
x39 = -57.5
x40 = -51.5
x41 = -93.5
x42 = 24.5
x43 = 84.5
x44 = -75.5
x45 = -3.5
x46 = 48.5
x47 = 86.5
x48 = 32.5
x49 = 66.5
x50 = 0.5
x51 = -23.5
x52 = -59.5
x53 = -45.5
x54 = 90.5
x55 = -87.5
x56 = 80.5
x57 = -33.5
x58 = -29.5
x59 = -11.5
x60 = 38.5
x61 = -81.5
x62 = 54.5
x63 = 62.5
x64 = -95.5
x65 = 14.5
x66 = -77.5
x67 = -5.5
x68 = 18.5
x68 = 18.5
The graph