Mister Exam
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How to use it?
- Equation:
-
Equation 2x=18-x
-
Equation x^4=(2*x-3)^2
-
Equation 9*x^2=54*x
-
Equation cos(x)+sin(x)=0
- Express {x} in terms of y where:
- -18*x-1*y=-11
- 7*x-2*y=20
- -1*x-20*y=-17
- -2*x-14*y=7
-
Identical expressions
- cos((pi*(8x- one)/ four))=sqtr two /2
- co sinus of e of (( Pi multiply by (8x minus 1) divide by 4)) equally sqtr2 divide by 2
- co sinus of e of (( Pi multiply by (8x minus one) divide by four)) equally sqtr two divide by 2
- cos((pi(8x-1)/4))=sqtr2/2
- cospi8x-1/4=sqtr2/2
- cos((pi*(8x-1) divide by 4))=sqtr2 divide by 2
-
Similar expressions
- cos((pi*(8x+1)/4))=sqtr2/2
cos((pi*(8x-1)/4))=sqtr2/2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
___ /pi*(8*x - 1)\ \/ 2 cos|------------| = ----- \ 4 / 2
$$\cos{\left(\frac{\pi \left(8 x - 1\right)}{4} \right)} = \frac{\sqrt{2}}{2}$$
Detail solution
Given the equation
$$\cos{\left(\frac{\pi \left(8 x - 1\right)}{4} \right)} = \frac{\sqrt{2}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$2 \pi x + \frac{\pi}{4} = 2 \pi n + \operatorname{asin}{\left(\frac{\sqrt{2}}{2} \right)}$$
$$2 \pi x + \frac{\pi}{4} = 2 \pi n - \operatorname{asin}{\left(\frac{\sqrt{2}}{2} \right)} + \pi$$
Or
$$2 \pi x + \frac{\pi}{4} = 2 \pi n + \frac{\pi}{4}$$
$$2 \pi x + \frac{\pi}{4} = 2 \pi n + \frac{3 \pi}{4}$$
, where n - is a integer
Move
$$\frac{\pi}{4}$$
to right part of the equation with the opposite sign, in total:
$$2 \pi x = 2 \pi n$$
$$2 \pi x = 2 \pi n + \frac{\pi}{2}$$
Divide both parts of the equation by
$$2 \pi$$
we get the answer:
$$x_{1} = n$$
$$x_{2} = \frac{2 \pi n + \frac{\pi}{2}}{2 \pi}$$
$$\cos{\left(\frac{\pi \left(8 x - 1\right)}{4} \right)} = \frac{\sqrt{2}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$2 \pi x + \frac{\pi}{4} = 2 \pi n + \operatorname{asin}{\left(\frac{\sqrt{2}}{2} \right)}$$
$$2 \pi x + \frac{\pi}{4} = 2 \pi n - \operatorname{asin}{\left(\frac{\sqrt{2}}{2} \right)} + \pi$$
Or
$$2 \pi x + \frac{\pi}{4} = 2 \pi n + \frac{\pi}{4}$$
$$2 \pi x + \frac{\pi}{4} = 2 \pi n + \frac{3 \pi}{4}$$
, where n - is a integer
Move
$$\frac{\pi}{4}$$
to right part of the equation with the opposite sign, in total:
$$2 \pi x = 2 \pi n$$
$$2 \pi x = 2 \pi n + \frac{\pi}{2}$$
Divide both parts of the equation by
$$2 \pi$$
we get the answer:
$$x_{1} = n$$
$$x_{2} = \frac{2 \pi n + \frac{\pi}{2}}{2 \pi}$$
Sum and product of roots
[src]
sum
0 + 1/4
$$\left(0\right) + \left(\frac{1}{4}\right)$$
=
1/4
$$\frac{1}{4}$$
product
0 * 1/4
$$\left(0\right) * \left(\frac{1}{4}\right)$$
=
0
$$0$$
Numerical answer
[src]
x1 = -15.75
x2 = -71.75
x3 = -69.75
x4 = 32.25
x5 = -65.75
x6 = -61.75
x7 = -39.75
x8 = -77.75
x9 = -23.0
x10 = -63.75
x11 = 40.25
x12 = -93.75
x13 = 96.25
x14 = 6.25
x15 = -91.75
x16 = 90.25
x17 = -27.75
x18 = -13.75
x19 = -97.75
x20 = -89.75
x21 = 10.25
x22 = 54.25
x23 = -23.75
x24 = -83.75
x25 = -21.75
x26 = 60.25
x27 = -41.75
x28 = 64.25
x29 = -57.75
x30 = 24.25
x31 = 80.25
x32 = -67.75
x33 = -87.75
x34 = 2.25
x35 = 46.25
x36 = -79.75
x37 = 12.25
x38 = -7.75
x39 = -5.75
x40 = -3.75
x41 = 88.25
x42 = -53.75
x43 = 56.25
x44 = 58.25
x45 = 23.25
x46 = -19.75
x47 = -51.75
x48 = 22.25
x49 = 52.25
x50 = 76.25
x51 = 72.25
x52 = -99.75
x53 = -95.75
x54 = -9.75
x55 = 36.25
x56 = 30.25
x57 = -73.75
x58 = -29.75
x59 = -45.75
x60 = -85.75
x61 = -47.75
x62 = -1.75
x63 = 4.25
x64 = 18.25
x65 = 92.25
x66 = -35.75
x67 = 78.25
x68 = 94.25
x69 = 66.25
x70 = 84.25
x71 = 100.25
x72 = 8.25
x73 = 38.25
x74 = 50.25
x75 = 82.25
x76 = -31.75
x77 = 28.25
x78 = -11.75
x79 = 34.25
x80 = 98.25
x81 = -75.75
x82 = -17.75
x83 = -49.75
x84 = -37.75
x85 = -25.75
x86 = -33.75
x87 = 20.25
x88 = -81.75
x89 = 74.0
x90 = 70.25
x91 = 0.0
x92 = -55.75
x93 = 62.25
x94 = 16.25
x95 = -59.75
x96 = 42.25
x97 = 68.25
x98 = 14.25
x99 = 48.25
x100 = 86.25
x101 = 26.25
x101 = 26.25
The graph