Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation sin(pi*x)=0
-
Equation 7x^3-28x=0
- Equation sqrt(x)-4root(4)(x)=5
- Equation 16-3|x|=4
- Express {x} in terms of y where:
- 8*x+7*y=-13
- -12*x+3*y=-9
- 14*x-16*y=14
- 9*x-18*y=6
- Derivative of:
-
sin(pi*x)
- Integral of d{x}:
- sin(pi*x)
- Graphing y =:
- sin(pi*x)
-
Identical expressions
- sin(pi*x)= zero
- sinus of ( Pi multiply by x) equally 0
- sinus of ( Pi multiply by x) equally zero
- sin(pix)=0
- sinpix=0
- sin(pi*x)=O
-
Similar expressions
- |6x-5|=4sin(pix/3)
- sin((pi*(x+9))/4)=sqrt(2)/(-2)
sin(pi*x)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sin{\left(\pi x \right)} = 0$$
- this is the simplest trigonometric equation
We get:
$$\sin{\left(\pi x \right)} = 0$$
This equation is transformed to
$$\pi x = 2 \pi n + \operatorname{asin}{\left(0 \right)}$$
$$\pi x = 2 \pi n - \operatorname{asin}{\left(0 \right)} + \pi$$
Or
$$\pi x = 2 \pi n$$
$$\pi x = 2 \pi n + \pi$$
, where n - is a integer
Divide both parts of the equation by
$$\pi$$
we get the answer:
$$x_{1} = 2 n$$
$$x_{2} = \frac{2 \pi n + \pi}{\pi}$$
$$\sin{\left(\pi x \right)} = 0$$
- this is the simplest trigonometric equation
with the change of sign in 0
We get:
$$\sin{\left(\pi x \right)} = 0$$
This equation is transformed to
$$\pi x = 2 \pi n + \operatorname{asin}{\left(0 \right)}$$
$$\pi x = 2 \pi n - \operatorname{asin}{\left(0 \right)} + \pi$$
Or
$$\pi x = 2 \pi n$$
$$\pi x = 2 \pi n + \pi$$
, where n - is a integer
Divide both parts of the equation by
$$\pi$$
we get the answer:
$$x_{1} = 2 n$$
$$x_{2} = \frac{2 \pi n + \pi}{\pi}$$
Numerical answer
[src]
x1 = -82.0
x2 = 76.0
x3 = 20.0
x4 = -50.0
x5 = 80.0
x6 = -4.0
x7 = -44.0
x8 = -66.0
x9 = 26.0
x10 = 98.0
x11 = 30.0
x12 = -10.0
x13 = 46.0
x14 = -56.0
x15 = -48.0
x16 = -62.0
x17 = 16.0
x18 = -46.0
x19 = -32.0
x20 = 66.0
x21 = -100.0
x22 = -18.0
x23 = -12.0
x24 = 18.0
x25 = -86.0
x26 = -26.0
x27 = 84.0
x28 = -38.0
x29 = 22.0
x30 = -14.0
x31 = 4.0
x32 = 12.0
x33 = -60.0
x34 = 52.0
x35 = 96.0
x36 = 92.0
x37 = -28.0
x38 = -58.0
x39 = -96.0
x40 = -94.0
x41 = 44.0
x42 = 88.0
x43 = 34.0
x44 = 32.0
x45 = -84.0
x46 = -8.0
x47 = 64.0
x48 = -98.0
x49 = -2.0
x50 = 74.0
x51 = -64.0
x52 = 0.0
x53 = -36.0
x54 = -74.0
x55 = 86.0
x56 = -34.0
x57 = 6.0
x58 = -42.0
x59 = -40.0
x60 = -24.0
x61 = 58.0
x62 = 28.0
x63 = 56.0
x64 = 54.0
x65 = -54.0
x66 = 62.0
x67 = -72.0
x68 = 40.0
x69 = -80.0
x70 = 72.0
x71 = 24.0
x72 = 82.0
x73 = -30.0
x74 = 94.0
x75 = -6.0
x76 = -22.0
x77 = 42.0
x78 = 10.0
x79 = 70.0
x80 = -70.0
x81 = 68.0
x82 = -92.0
x83 = 78.0
x84 = 14.0
x85 = 90.0
x86 = 36.0
x87 = -76.0
x88 = 48.0
x89 = 38.0
x90 = -68.0
x91 = 100.0
x92 = -52.0
x93 = -88.0
x94 = -90.0
x95 = 2.0
x96 = -78.0
x97 = -20.0
x98 = 60.0
x99 = 8.0
x100 = 50.0
x101 = -16.0
x101 = -16.0
The graph