Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation (x+10)^2=(5-x)^2
-
Equation tg(x)=0
-
Equation x^2-5x=0
-
Equation 3(4-2x)+6=-2x+4
- Express {x} in terms of y where:
- -10*x-16*y=-6
- 16*x+7*y=8
- -11*x+4*y=-8
- 17*x-11*y=2
- Sum of series:
-
1/2
- Integral of d{x}:
-
1/2
- Derivative of:
-
1/2
-
Identical expressions
- sin*(pi(*5x+ fifteen)/ six)= one / two
- sinus of multiply by ( Pi ( multiply by 5x plus 15) divide by 6) equally 1 divide by 2
- sinus of multiply by ( Pi ( multiply by 5x plus fifteen) divide by six) equally one divide by two
- sin(pi(5x+15)/6)=1/2
- sinpi5x+15/6=1/2
- sin*(pi(*5x+15) divide by 6)=1 divide by 2
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Similar expressions
- sinpi(5*x+15)/6=1/2
- sin*(pi(*5x-15)/6)=1/2
sin*(pi(*5x+15)/6)=1/2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
/pi*(5*x + 15)\ sin|-------------| = 1/2 \ 6 /
$$\sin{\left(\frac{\pi \left(5 x + 15\right)}{6} \right)} = \frac{1}{2}$$
Detail solution
Given the equation
$$\sin{\left(\frac{\pi \left(5 x + 15\right)}{6} \right)} = \frac{1}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{5 \pi x}{6} = \pi n + \operatorname{acos}{\left(\frac{1}{2} \right)}$$
$$\frac{5 \pi x}{6} = \pi n - \pi + \operatorname{acos}{\left(\frac{1}{2} \right)}$$
Or
$$\frac{5 \pi x}{6} = \pi n + \frac{\pi}{3}$$
$$\frac{5 \pi x}{6} = \pi n - \frac{2 \pi}{3}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{5 \pi}{6}$$
we get the answer:
$$x_{1} = \frac{6 \left(\pi n + \frac{\pi}{3}\right)}{5 \pi}$$
$$x_{2} = \frac{6 \left(\pi n - \frac{2 \pi}{3}\right)}{5 \pi}$$
$$\sin{\left(\frac{\pi \left(5 x + 15\right)}{6} \right)} = \frac{1}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{5 \pi x}{6} = \pi n + \operatorname{acos}{\left(\frac{1}{2} \right)}$$
$$\frac{5 \pi x}{6} = \pi n - \pi + \operatorname{acos}{\left(\frac{1}{2} \right)}$$
Or
$$\frac{5 \pi x}{6} = \pi n + \frac{\pi}{3}$$
$$\frac{5 \pi x}{6} = \pi n - \frac{2 \pi}{3}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{5 \pi}{6}$$
we get the answer:
$$x_{1} = \frac{6 \left(\pi n + \frac{\pi}{3}\right)}{5 \pi}$$
$$x_{2} = \frac{6 \left(\pi n - \frac{2 \pi}{3}\right)}{5 \pi}$$
Sum and product of roots
[src]
sum
2 + 2/5
$$\frac{2}{5} + 2$$
=
12/5
$$\frac{12}{5}$$
product
2*2 --- 5
$$\frac{2 \cdot 2}{5}$$
=
4/5
$$\frac{4}{5}$$
4/5
Numerical answer
[src]
x1 = 74.0
x2 = 4.4
x3 = 122.8
x4 = 74.8
x5 = 88.4
x6 = 82.0
x7 = -62.0
x8 = 94.0
x9 = -55.6
x10 = -100.4
x11 = 26.0
x12 = 158.8
x13 = -34.0
x14 = -67.6
x15 = 48.4
x16 = 86.8
x17 = -26.0
x18 = 50.8
x19 = 96.4
x20 = 19.6
x21 = 10.0
x22 = -46.0
x23 = 14.0
x24 = 146.8
x25 = 62.8
x26 = 84.4
x27 = -82.0
x28 = 52.4
x29 = -76.4
x30 = -74.0
x31 = 38.8
x32 = 67.6
x33 = -83.6
x34 = 86.0
x35 = 91.6
x36 = -50.0
x37 = -47.6
x38 = 31.6
x39 = 50.0
x40 = 16.4
x41 = -28.4
x42 = 28.4
x43 = -58.0
x44 = -88.4
x45 = -7.6
x46 = -40.4
x47 = 64.4
x48 = 2.0
x49 = 46.0
x50 = -38.0
x51 = -70.0
x52 = -11.6
x53 = 40.4
x54 = 76.4
x55 = 0.4
x56 = 60.4
x57 = 7.6
x58 = -23.6
x59 = -35.6
x60 = 206.8
x61 = -94.0
x62 = 72.4
x63 = -59.6
x64 = 36.4
x65 = -64.4
x66 = 182.8
x67 = 194.8
x68 = 43.6
x69 = 12.4
x70 = -91.6
x71 = -2.0
x72 = 34.0
x73 = 100.4
x74 = -16.4
x75 = -43.6
x76 = 58.0
x77 = -71.6
x78 = -98.0
x79 = -79.6
x80 = 79.6
x81 = 38.0
x82 = -22.0
x83 = 170.8
x84 = 62.0
x85 = -86.0
x86 = 134.8
x87 = -14.0
x88 = -52.4
x89 = -4.4
x90 = 98.8
x91 = 70.0
x92 = 98.0
x93 = 55.6
x94 = -19.6
x95 = 218.8
x96 = -31.6
x97 = 24.4
x98 = 110.8
x99 = -10.0
x100 = -95.6
x101 = 22.0
x101 = 22.0