Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation cos(pi*x)=0
- Equation (ctgx+3)^2+2a^3+3a^2=(a^2+2a+3)*(ctgx+3)
- Equation √3(cos4x+1)=2(2-cos4x)cos2x
-
Equation tg(x)=3
- Express {x} in terms of y where:
- (x^2+y^2-1)^3+x^2*y^3=0
- -1*x-19*y=-10
- 5*x+5*y=20
- 4*x-16*y=6
- Limit of the function:
-
cos(pi*x)
- Graphing y =:
- cos(pi*x)
- cos(pi*x)
-
Identical expressions
- cos(pi*x)= zero
- co sinus of e of ( Pi multiply by x) equally 0
- co sinus of e of ( Pi multiply by x) equally zero
- cos(pix)=0
- cospix=0
- cos(pi*x)=O
-
Similar expressions
- 2sin^2pix/12-3cospix/12=0
- cos(pi*(x-1)/3)=1/2
- cos((pi*(x+1))/4)=sqrt(2)/2
- cos(pi(x+1))/2=-1
cos(pi*x)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\cos{\left(\pi x \right)} = 0$$
- this is the simplest trigonometric equation
We get:
$$\cos{\left(\pi x \right)} = 0$$
This equation is transformed to
$$\pi x = \pi n + \operatorname{acos}{\left(0 \right)}$$
$$\pi x = \pi n - \pi + \operatorname{acos}{\left(0 \right)}$$
Or
$$\pi x = \pi n + \frac{\pi}{2}$$
$$\pi x = \pi n - \frac{\pi}{2}$$
, where n - is a integer
Divide both parts of the equation by
$$\pi$$
we get the answer:
$$x_{1} = \frac{\pi n + \frac{\pi}{2}}{\pi}$$
$$x_{2} = \frac{\pi n - \frac{\pi}{2}}{\pi}$$
$$\cos{\left(\pi x \right)} = 0$$
- this is the simplest trigonometric equation
with the change of sign in 0
We get:
$$\cos{\left(\pi x \right)} = 0$$
This equation is transformed to
$$\pi x = \pi n + \operatorname{acos}{\left(0 \right)}$$
$$\pi x = \pi n - \pi + \operatorname{acos}{\left(0 \right)}$$
Or
$$\pi x = \pi n + \frac{\pi}{2}$$
$$\pi x = \pi n - \frac{\pi}{2}$$
, where n - is a integer
Divide both parts of the equation by
$$\pi$$
we get the answer:
$$x_{1} = \frac{\pi n + \frac{\pi}{2}}{\pi}$$
$$x_{2} = \frac{\pi n - \frac{\pi}{2}}{\pi}$$
Sum and product of roots
[src]
sum
0 + 1/2 + 3/2
$$\left(0 + \frac{1}{2}\right) + \frac{3}{2}$$
=
2
$$2$$
product
1*1/2*3/2
$$1 \cdot \frac{1}{2} \cdot \frac{3}{2}$$
=
3/4
$$\frac{3}{4}$$
3/4
Numerical answer
[src]
x1 = 32.5
x2 = 70.5
x3 = -3.5
x4 = 16.5
x5 = 86.5
x6 = -55.5
x7 = 48.5
x8 = 76.5
x9 = 60.5
x10 = -7.5
x11 = -23.5
x12 = -95.5
x13 = -53.5
x14 = 62.5
x15 = 52.5
x16 = -49.5
x17 = -19.5
x18 = 40.5
x19 = 28.5
x20 = -1.5
x21 = 58.5
x22 = 50.5
x23 = 30.5
x24 = -9.5
x25 = -71.5
x26 = -57.5
x27 = -63.5
x28 = -41.5
x29 = -65.5
x30 = -89.5
x31 = -15.5
x32 = -13.5
x33 = 24.5
x34 = 42.5
x35 = 12.5
x36 = 2.5
x37 = -47.5
x38 = 18.5
x39 = 94.5
x40 = -35.5
x41 = 78.5
x42 = 6.5
x43 = 56.5
x44 = -81.5
x45 = -99.5
x46 = -93.5
x47 = -11.5
x48 = 84.5
x49 = 90.5
x50 = 54.5
x51 = 8.5
x52 = 38.5
x53 = -73.5
x54 = 96.5
x55 = 82.5
x56 = -21.5
x57 = -29.5
x58 = -43.5
x59 = -17.5
x60 = 64.5
x61 = 10.5
x62 = 98.5
x63 = 100.5
x64 = -97.5
x65 = 34.5
x66 = -25.5
x67 = -85.5
x68 = 74.5
x69 = -69.5
x70 = 46.5
x71 = -31.5
x72 = -77.5
x73 = -75.5
x74 = 80.5
x75 = 92.5
x76 = -67.5
x77 = -33.5
x78 = 72.5
x79 = 0.5
x80 = -87.5
x81 = -37.5
x82 = -83.5
x83 = -39.5
x84 = 68.5
x85 = -45.5
x86 = 36.5
x87 = 22.5
x88 = -61.5
x89 = 88.5
x90 = 4.5
x91 = 20.5
x92 = 44.5
x93 = -27.5
x94 = -5.5
x95 = -59.5
x96 = 14.5
x97 = 26.5
x98 = -91.5
x99 = -79.5
x100 = -51.5
x101 = 66.5
x101 = 66.5
The graph