Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 5*x^2=35*x
-
Equation 2,4(x+0,98)=4,08
-
Equation x+14=8
-
Equation -x/11+x=50/11
- Express {x} in terms of y where:
- 8*x-16*y=14
- 15*x-3*y=19
- 11*x+8*y=-16
- -11*x-1*y=12
- Derivative of:
-
sin(pi*x)
-
-1
- Integral of d{x}:
- sin(pi*x)
-
-1
- Graphing y =:
- sin(pi*x)
- Sum of series:
-
-1
-
Identical expressions
- sin(pi*x)=- one
- sinus of ( Pi multiply by x) equally minus 1
- sinus of ( Pi multiply by x) equally minus one
- sin(pix)=-1
- sinpix=-1
-
Similar expressions
- sin((pi*x)/4)=-1
- sin(pi*x)=+1
- sin(pi*x/7)=0
- log4(x^2-8x+20)=sin((pi*x)/8)
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
$$\pi x = 2 \pi n - \frac{\pi}{2}$$
$$\pi x = 2 \pi n + \frac{3 \pi}{2}$$
, where n - is a integer
Divide both parts of the equation by
$$\pi$$
we get the answer:
$$x_{1} = \frac{2 \pi n - \frac{\pi}{2}}{\pi}$$
$$x_{2} = \frac{2 \pi n + \frac{3 \pi}{2}}{\pi}$$
$$\sin{\left(\pi x \right)} = -1$$
- 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
$$\pi x = 2 \pi n - \frac{\pi}{2}$$
$$\pi x = 2 \pi n + \frac{3 \pi}{2}$$
, where n - is a integer
Divide both parts of the equation by
$$\pi$$
we get the answer:
$$x_{1} = \frac{2 \pi n - \frac{\pi}{2}}{\pi}$$
$$x_{2} = \frac{2 \pi n + \frac{3 \pi}{2}}{\pi}$$
Sum and product of roots
[src]
sum
-1/2 + 3/2
$$- \frac{1}{2} + \frac{3}{2}$$
=
1
$$1$$
product
-3 --- 2*2
$$- \frac{3}{4}$$
=
-3/4
$$- \frac{3}{4}$$
-3/4
Numerical answer
[src]
x1 = 75.5000001413479
x2 = -66.4999998586521
x3 = -56.4999998586521
x4 = 65.5000001413479
x5 = 51.5000001413479
x6 = 21.5000001413479
x7 = -100.499999858652
x8 = 89.5000001413479
x9 = 31.5000001413479
x10 = -8.49999985865214
x11 = 91.5000001413479
x12 = -4.49999985865214
x13 = -30.4999998586521
x14 = -10.4999998586521
x15 = -22.4999998586521
x16 = -64.4999998586521
x17 = 67.5000001413479
x18 = 55.5000001413479
x19 = -70.4999998586521
x20 = -28.4999998586521
x21 = 61.5000001413479
x22 = -24.4999998586521
x23 = 47.5000001413479
x24 = -46.4999998586521
x25 = -80.4999998586521
x26 = -42.4999998586521
x27 = 81.5000001413479
x28 = -76.4999998586521
x29 = 41.5000001413479
x30 = -12.4999998586521
x31 = 97.5000001413479
x32 = -18.4999998586521
x33 = 53.5000001413479
x34 = -94.4999998586521
x35 = -78.4999998586521
x36 = 9.50000014134786
x37 = 29.5000001413479
x38 = -96.4999998586521
x39 = -6.49999985865214
x40 = -20.4999998586521
x41 = 69.5000001413479
x42 = -50.4999998586521
x43 = -60.4999998586521
x44 = 95.5000001413479
x45 = -62.4999998586521
x46 = 93.5000001413479
x47 = -32.4999998586521
x48 = -98.4999998586521
x49 = -2.49999985865214
x50 = 7.50000014134786
x51 = 43.5000001413479
x52 = 73.5000001413479
x53 = 11.5000001413479
x54 = -40.4999998586521
x55 = 45.5000001413479
x56 = 57.5000001413479
x57 = -38.4999998586521
x58 = -88.4999998586521
x59 = -34.4999998586521
x60 = 13.5000001413479
x61 = 27.5000001413479
x62 = -52.4999998586521
x63 = 87.5000001413479
x64 = 5.50000014134786
x65 = 63.5000001413479
x66 = 23.5000001413479
x67 = 39.5000001413479
x68 = -48.4999998586521
x69 = -84.4999998586521
x70 = 83.5000001413479
x71 = -44.4999998586521
x72 = 37.5000001413479
x73 = 19.5000001413479
x74 = -92.4999998586521
x75 = 1.50000014134786
x76 = 85.5000001413479
x77 = -90.4999998586521
x78 = 71.5000001413479
x79 = 17.5000001413479
x80 = -54.4999998586521
x81 = 35.5000001413479
x82 = -68.4999998586521
x83 = 15.5000001413479
x84 = 3.50000014134786
x85 = 59.5000001413479
x86 = -36.4999998586521
x87 = 33.5000001413479
x88 = 49.5000001413479
x89 = -86.4999998586521
x90 = 99.5000001413479
x91 = 77.5000001413479
x92 = -82.4999998586521
x93 = -16.4999998586521
x94 = -14.4999998586521
x95 = -26.4999998586521
x96 = -74.4999998586521
x97 = -0.499999858652136
x98 = -72.4999998586521
x99 = -58.4999998586521
x100 = 25.5000001413479
x101 = 79.5000001413479
x101 = 79.5000001413479
The graph