Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 9(x-1)=x+15
-
Equation sin(x/3)=1/2
-
Equation x^2=12
-
Equation 3*x=8
- Express {x} in terms of y where:
- 10*x-15*y=16
- 5*x+12*y=18
- 15*x+7*y=2
- 12*x-20*y=10
-
Identical expressions
- sin(x*(3pi)/ two)= zero
- sinus of (x multiply by (3 Pi ) divide by 2) equally 0
- sinus of (x multiply by (3 Pi ) divide by two) equally zero
- sin(x(3pi)/2)=0
- sinx3pi/2=0
- sin(x*(3pi)/2)=O
- sin(x*(3pi) divide by 2)=0
-
Similar expressions
- 3cos^2x+8sinx*(3pi/2-x)-5=0
sin(x*(3pi)/2)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sin{\left(\frac{3 \pi x}{2} \right)} = 0$$
- this is the simplest trigonometric equation
We get:
$$\sin{\left(\frac{3 \pi x}{2} \right)} = 0$$
This equation is transformed to
$$\frac{3 \pi x}{2} = 2 \pi n + \operatorname{asin}{\left(0 \right)}$$
$$\frac{3 \pi x}{2} = 2 \pi n - \operatorname{asin}{\left(0 \right)} + \pi$$
Or
$$\frac{3 \pi x}{2} = 2 \pi n$$
$$\frac{3 \pi x}{2} = 2 \pi n + \pi$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{3 \pi}{2}$$
we get the answer:
$$x_{1} = \frac{4 n}{3}$$
$$x_{2} = \frac{2 \left(2 \pi n + \pi\right)}{3 \pi}$$
$$\sin{\left(\frac{3 \pi x}{2} \right)} = 0$$
- this is the simplest trigonometric equation
with the change of sign in 0
We get:
$$\sin{\left(\frac{3 \pi x}{2} \right)} = 0$$
This equation is transformed to
$$\frac{3 \pi x}{2} = 2 \pi n + \operatorname{asin}{\left(0 \right)}$$
$$\frac{3 \pi x}{2} = 2 \pi n - \operatorname{asin}{\left(0 \right)} + \pi$$
Or
$$\frac{3 \pi x}{2} = 2 \pi n$$
$$\frac{3 \pi x}{2} = 2 \pi n + \pi$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{3 \pi}{2}$$
we get the answer:
$$x_{1} = \frac{4 n}{3}$$
$$x_{2} = \frac{2 \left(2 \pi n + \pi\right)}{3 \pi}$$
Sum and product of roots
[src]
sum
2/3
$$\frac{2}{3}$$
=
2/3
$$\frac{2}{3}$$
product
0*2 --- 3
$$\frac{0 \cdot 2}{3}$$
=
0
$$0$$
0
Numerical answer
[src]
x1 = -42.0
x2 = 82.0
x3 = -66.0
x4 = 76.0
x5 = 4.0
x6 = -30.0
x7 = 16.0
x8 = -22.0
x9 = -76.0
x10 = 88.0
x11 = 62.0
x12 = 8.0
x13 = 66.0
x14 = 92.0
x15 = -62.0
x16 = 94.0
x17 = 26.0
x18 = 46.0
x19 = 22.0
x20 = -78.0
x21 = -48.0
x22 = 100.0
x23 = -60.0
x24 = -90.0
x25 = -6.0
x26 = 12.0
x27 = 32.0
x28 = 30.0
x29 = -34.0
x30 = -20.0
x31 = -52.0
x32 = -96.0
x33 = -64.0
x34 = 68.0
x35 = 72.0
x36 = 50.0
x37 = -82.0
x38 = -72.0
x39 = -24.0
x40 = 52.0
x41 = -10.0
x42 = -8.0
x43 = 10.0
x44 = 84.0
x45 = -28.0
x46 = -84.0
x47 = 24.0
x48 = 64.0
x49 = 36.0
x50 = -88.0
x51 = -2.0
x52 = 14.0
x53 = -38.0
x54 = 60.0
x55 = 56.0
x56 = -86.0
x57 = 40.0
x58 = -46.0
x59 = -74.0
x60 = -26.0
x61 = -32.0
x62 = 58.0
x63 = 70.0
x64 = -70.0
x65 = 18.0
x66 = -68.0
x67 = -14.0
x68 = 44.0
x69 = 6.0
x70 = -54.0
x71 = -58.0
x72 = 90.0
x73 = 98.0
x74 = -92.0
x75 = -94.0
x76 = 80.0
x77 = 86.0
x78 = -44.0
x79 = -18.0
x80 = 0.0
x81 = 48.0
x82 = 96.0
x83 = -80.0
x84 = -16.0
x85 = 20.0
x86 = -12.0
x87 = -56.0
x88 = 34.0
x89 = -40.0
x90 = -50.0
x91 = 28.0
x92 = 2.0
x93 = -36.0
x94 = 74.0
x95 = 42.0
x96 = 54.0
x97 = -98.0
x98 = -4.0
x99 = -100.0
x100 = 78.0
x101 = 38.0
x101 = 38.0