Mister Exam
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How to use it?
- Equation:
-
Equation 20-7(5x-4)=6
- Equation sin((pi*(8*x+5)/6))=sqrt(3)/2
- Equation 3x^2-75=0
-
Equation k^2-5*k+6=0
- Express {x} in terms of y where:
- -1*x-19*y=-10
- 5*x+5*y=20
- 4*x-16*y=6
- sqrt(x^2+y^2+4x-6y-12)+(x^2+10x-27)=8-|y-9|+|y-3|
- Derivative of:
-
sqrt(3)/2
- Limit of the function:
-
sqrt(3)/2
-
Identical expressions
- sin((pi*(eight *x+ five)/ six))=sqrt(three)/ two
- sinus of (( Pi multiply by (8 multiply by x plus 5) divide by 6)) equally square root of (3) divide by 2
- sinus of (( Pi multiply by (eight multiply by x plus five) divide by six)) equally square root of (three) divide by two
- sin((pi*(8*x+5)/6))=√(3)/2
- sin((pi(8x+5)/6))=sqrt(3)/2
- sinpi8x+5/6=sqrt3/2
- sin((pi*(8*x+5) divide by 6))=sqrt(3) divide by 2
-
Similar expressions
- tg(x)=sqrt3/2
- sin(3x)=-sqrt3/2
- sin((pi*(8*x-5)/6))=sqrt(3)/2
- sin2x=-(sqrt3/2)
- sin(0.5x)=-sqrt3/2
sin((pi*(8*x+5)/6))=sqrt(3)/2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
___ /pi*(8*x + 5)\ \/ 3 sin|------------| = ----- \ 6 / 2
$$\sin{\left(\frac{\pi \left(8 x + 5\right)}{6} \right)} = \frac{\sqrt{3}}{2}$$
Detail solution
Given the equation
$$\sin{\left(\frac{\pi \left(8 x + 5\right)}{6} \right)} = \frac{\sqrt{3}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{4 \pi x}{3} + \frac{\pi}{3} = \pi n + \operatorname{acos}{\left(\frac{\sqrt{3}}{2} \right)}$$
$$\frac{4 \pi x}{3} + \frac{\pi}{3} = \pi n - \pi + \operatorname{acos}{\left(\frac{\sqrt{3}}{2} \right)}$$
Or
$$\frac{4 \pi x}{3} + \frac{\pi}{3} = \pi n + \frac{\pi}{6}$$
$$\frac{4 \pi x}{3} + \frac{\pi}{3} = \pi n - \frac{5 \pi}{6}$$
, where n - is a integer
Move
$$\frac{\pi}{3}$$
to right part of the equation
with the opposite sign, in total:
$$\frac{4 \pi x}{3} = \pi n - \frac{\pi}{6}$$
$$\frac{4 \pi x}{3} = \pi n - \frac{7 \pi}{6}$$
Divide both parts of the equation by
$$\frac{4 \pi}{3}$$
we get the answer:
$$x_{1} = \frac{3 \left(\pi n - \frac{\pi}{6}\right)}{4 \pi}$$
$$x_{2} = \frac{3 \left(\pi n - \frac{7 \pi}{6}\right)}{4 \pi}$$
$$\sin{\left(\frac{\pi \left(8 x + 5\right)}{6} \right)} = \frac{\sqrt{3}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{4 \pi x}{3} + \frac{\pi}{3} = \pi n + \operatorname{acos}{\left(\frac{\sqrt{3}}{2} \right)}$$
$$\frac{4 \pi x}{3} + \frac{\pi}{3} = \pi n - \pi + \operatorname{acos}{\left(\frac{\sqrt{3}}{2} \right)}$$
Or
$$\frac{4 \pi x}{3} + \frac{\pi}{3} = \pi n + \frac{\pi}{6}$$
$$\frac{4 \pi x}{3} + \frac{\pi}{3} = \pi n - \frac{5 \pi}{6}$$
, where n - is a integer
Move
$$\frac{\pi}{3}$$
to right part of the equation
with the opposite sign, in total:
$$\frac{4 \pi x}{3} = \pi n - \frac{\pi}{6}$$
$$\frac{4 \pi x}{3} = \pi n - \frac{7 \pi}{6}$$
Divide both parts of the equation by
$$\frac{4 \pi}{3}$$
we get the answer:
$$x_{1} = \frac{3 \left(\pi n - \frac{\pi}{6}\right)}{4 \pi}$$
$$x_{2} = \frac{3 \left(\pi n - \frac{7 \pi}{6}\right)}{4 \pi}$$
Sum and product of roots
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sum
-1/8 + 9/8
$$- \frac{1}{8} + \frac{9}{8}$$
=
1
$$1$$
product
-9 --- 8*8
$$- \frac{9}{64}$$
=
-9/64
$$- \frac{9}{64}$$
-9/64
Numerical answer
[src]
x1 = -61.875
x2 = 88.125
x3 = -99.125
x4 = 32.875
x5 = -30.125
x6 = 5.875
x7 = 92.875
x8 = 20.875
x9 = -42.125
x10 = 76.125
x11 = 44.875
x12 = -87.125
x13 = -66.125
x14 = -73.875
x15 = 14.875
x16 = 56.875
x17 = -21.125
x18 = -36.125
x19 = 53.875
x20 = 95.875
x21 = -69.125
x22 = -49.875
x23 = 34.125
x24 = -3.125
x25 = -18.125
x26 = 41.875
x27 = -48.125
x28 = -96.125
x29 = 17.875
x30 = 77.875
x31 = -67.875
x32 = 70.125
x33 = 59.875
x34 = 94.125
x35 = 46.125
x36 = -25.875
x37 = 71.875
x38 = 80.875
x39 = 38.875
x40 = 22.125
x41 = -33.125
x42 = 89.875
x43 = 35.875
x44 = -1.875
x45 = -51.125
x46 = 74.875
x47 = 86.875
x48 = -27.125
x49 = 64.125
x50 = 28.125
x51 = -78.125
x52 = 50.875
x53 = 10.125
x54 = -84.125
x55 = -79.875
x56 = -37.875
x57 = 100.125
x58 = 65.875
x59 = -24.125
x60 = -75.125
x61 = -60.125
x62 = -90.125
x63 = -54.125
x64 = 26.875
x65 = 47.875
x66 = -97.875
x67 = 29.875
x68 = -12.125
x69 = -81.125
x70 = -39.125
x71 = -0.125
x72 = 2.875
x73 = -15.125
x74 = -13.875
x75 = -57.125
x76 = 16.125
x77 = -19.875
x78 = -72.125
x79 = 40.125
x80 = -91.875
x81 = -43.875
x82 = -7.875
x83 = 4.125
x84 = 98.875
x85 = 83.875
x86 = -31.875
x87 = 68.875
x88 = -85.875
x89 = 82.125
x90 = -6.125
x91 = -93.125
x92 = -55.875
x93 = 62.875
x94 = 8.875
x95 = 11.875
x96 = 58.125
x97 = -9.125
x98 = -45.125
x99 = 23.875
x100 = -63.125
x101 = 52.125
x101 = 52.125