Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation x=x/2+1
-
Equation 1-7(4+2x)=-9-4x
-
Equation (x+9)^2=(x+6)^2
-
Equation sin(pi*x)=1
- Express {x} in terms of y where:
- -16*x-7*y=-5
- -1*x-7*y=5
- -4*x-18*y=-14
- 10*x+9*y=-4
- Derivative of:
-
sin(pi*x)
- Integral of d{x}:
- sin(pi*x)
- Graphing y =:
- sin(pi*x)
-
Identical expressions
- sin(pi*x)= one
- sinus of ( Pi multiply by x) equally 1
- sinus of ( Pi multiply by x) equally one
- sin(pix)=1
- sinpix=1
-
Similar expressions
- sin*(pi*x)/3=0,5
- |6x-5|=4sin(pix/3)
- sin(pi*x/4)+1=cos(pi*x/8)+2^(1/2)*cos((pi*x/8)-(pi/4))
- log2(x^2-2x+5)=2sin(pix/2)
sin(pi*x)=1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sin{\left(\pi x \right)} = 1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\pi x = 2 \pi n + \operatorname{asin}{\left(1 \right)}$$
$$\pi x = 2 \pi n - \operatorname{asin}{\left(1 \right)} + \pi$$
Or
$$\pi x = 2 \pi n + \frac{\pi}{2}$$
$$\pi x = 2 \pi n + \frac{\pi}{2}$$
, where n - is a integer
Divide both parts of the equation by
$$\pi$$
we get the answer:
$$x_{1} = \frac{2 \pi n + \frac{\pi}{2}}{\pi}$$
$$x_{2} = \frac{2 \pi n + \frac{\pi}{2}}{\pi}$$
$$\sin{\left(\pi x \right)} = 1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\pi x = 2 \pi n + \operatorname{asin}{\left(1 \right)}$$
$$\pi x = 2 \pi n - \operatorname{asin}{\left(1 \right)} + \pi$$
Or
$$\pi x = 2 \pi n + \frac{\pi}{2}$$
$$\pi x = 2 \pi n + \frac{\pi}{2}$$
, where n - is a integer
Divide both parts of the equation by
$$\pi$$
we get the answer:
$$x_{1} = \frac{2 \pi n + \frac{\pi}{2}}{\pi}$$
$$x_{2} = \frac{2 \pi n + \frac{\pi}{2}}{\pi}$$
Sum and product of roots
[src]
sum
0 + 1/2
$$0 + \frac{1}{2}$$
=
1/2
$$\frac{1}{2}$$
product
1*1/2
$$1 \cdot \frac{1}{2}$$
=
1/2
$$\frac{1}{2}$$
1/2
Numerical answer
[src]
x1 = -73.5000001246852
x2 = 74.4999998753148
x3 = 58.4999998753148
x4 = 8.49999987531485
x5 = -87.5000001246852
x6 = 96.4999998753148
x7 = -7.50000012468516
x8 = -25.5000001246852
x9 = -49.5000001246852
x10 = 64.4999998753148
x11 = 82.4999998753148
x12 = -79.5000001246852
x13 = 70.4999998753148
x14 = -53.5000001246852
x15 = 54.4999998753148
x16 = -89.5000001246852
x17 = 46.4999998753148
x18 = 88.4999998753148
x19 = -41.5000001246852
x20 = -77.5000001246852
x21 = 24.4999998753148
x22 = -45.5000001246852
x23 = 56.4999998753148
x24 = 80.4999998753148
x25 = -95.5000001246852
x26 = -39.5000001246852
x27 = -19.5000001246852
x28 = -17.5000001246852
x29 = -11.5000001246852
x30 = 6.49999987531484
x31 = -61.5000001246852
x32 = 18.4999998753148
x33 = -97.5000001246852
x34 = -37.5000001246852
x35 = -69.5000001246852
x36 = -63.5000001246852
x37 = 60.4999998753148
x38 = 32.4999998753148
x39 = -75.5000001246852
x40 = -15.5000001246852
x41 = -65.5000001246852
x42 = 16.4999998753148
x43 = 28.4999998753148
x44 = 14.4999998753148
x45 = 72.4999998753148
x46 = 92.4999998753148
x47 = -99.5000001246852
x48 = 50.4999998753148
x49 = -33.5000001246852
x50 = -59.5000001246852
x51 = -21.5000001246852
x52 = -13.5000001246852
x53 = 38.4999998753148
x54 = -27.5000001246852
x55 = -55.5000001246852
x56 = -23.5000001246852
x57 = 34.4999998753148
x58 = -35.5000001246852
x59 = 78.4999998753148
x60 = 26.4999998753148
x61 = 48.4999998753148
x62 = 36.4999998753148
x63 = 22.4999998753148
x64 = -1.50000012468516
x65 = 12.4999998753148
x66 = -5.50000012468516
x67 = 76.4999998753148
x68 = 42.4999998753148
x69 = 2.49999987531484
x70 = 94.4999998753148
x71 = -31.5000001246852
x72 = -67.5000001246852
x73 = -47.5000001246852
x74 = 44.4999998753148
x75 = -57.5000001246852
x76 = -83.5000001246852
x77 = 30.4999998753148
x78 = 98.4999998753148
x79 = 90.4999998753148
x80 = -29.5000001246852
x81 = -51.5000001246852
x82 = 4.49999987531484
x83 = -81.5000001246852
x84 = -43.5000001246852
x85 = 62.4999998753148
x86 = 84.4999998753148
x87 = 68.4999998753148
x88 = 20.4999998753148
x89 = 52.4999998753148
x90 = 40.4999998753148
x91 = 66.4999998753148
x92 = -9.50000012468515
x93 = -85.5000001246852
x94 = -3.50000012468516
x95 = -71.5000001246852
x96 = 100.499999875315
x97 = -93.5000001246852
x98 = 86.4999998753148
x99 = 0.499999875314845
x100 = 10.4999998753148
x101 = -91.5000001246852
x101 = -91.5000001246852
The graph