Mister Exam
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How to use it?
- Equation:
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Equation sqrt(2)sinx+1=0
- Equation ctg(x)=(√3/3)
- Equation x/24+11/24=23/24
-
Equation sqrt(118-39x)=8-3x
- Express {x} in terms of y where:
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Identical expressions
- sqrt(two)sinx+ one = zero
- square root of (2) sinus of x plus 1 equally 0
- square root of (two) sinus of x plus one equally zero
- √(2)sinx+1=0
- sqrt2sinx+1=0
- sqrt(2)sinx+1=O
-
Similar expressions
- (sqrt2*sin(x)+1)*(sqrt(-5cos(x)))=0
- cos(2*x)+sqrt(2)*sin(x)+1=0
- sqrt(2)sinx-1=0
sqrt(2)sinx+1=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sqrt{2} \sin{\left(x \right)} + 1 = 0$$
- this is the simplest trigonometric equation
Move $1$ to right part of the equation
with the change of sign in $1$
We get:
$$\sqrt{2} \sin{\left(x \right)} = -1$$
Divide both parts of the equation by $\sqrt{2}$
The equation is transformed to
$$\sin{\left(x \right)} = - \frac{\sqrt{2}}{2}$$
This equation is transformed to
$$x = 2 \pi n + \operatorname{asin}{\left(- \frac{\sqrt{2}}{2} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(- \frac{\sqrt{2}}{2} \right)} + \pi$$
Or
$$x = 2 \pi n - \frac{\pi}{4}$$
$$x = 2 \pi n + \frac{5 \pi}{4}$$
, where n - is a integer
$$\sqrt{2} \sin{\left(x \right)} + 1 = 0$$
- this is the simplest trigonometric equation
Move $1$ to right part of the equation
with the change of sign in $1$
We get:
$$\sqrt{2} \sin{\left(x \right)} = -1$$
Divide both parts of the equation by $\sqrt{2}$
The equation is transformed to
$$\sin{\left(x \right)} = - \frac{\sqrt{2}}{2}$$
This equation is transformed to
$$x = 2 \pi n + \operatorname{asin}{\left(- \frac{\sqrt{2}}{2} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(- \frac{\sqrt{2}}{2} \right)} + \pi$$
Or
$$x = 2 \pi n - \frac{\pi}{4}$$
$$x = 2 \pi n + \frac{5 \pi}{4}$$
, where n - is a integer
Rapid solution
[src]
-pi
x_1 = ----
4
$$x_{1} = - \frac{\pi}{4}$$
5*pi
x_2 = ----
4
$$x_{2} = \frac{5 \pi}{4}$$
Sum and product of roots
[src]
sum
-pi 5*pi ---- + ---- 4 4
$$\left(- \frac{\pi}{4}\right) + \left(\frac{5 \pi}{4}\right)$$
=
pi
$$\pi$$
product
-pi 5*pi ---- * ---- 4 4
$$\left(- \frac{\pi}{4}\right) * \left(\frac{5 \pi}{4}\right)$$
=
2 -5*pi ------ 16
$$- \frac{5 \pi^{2}}{16}$$
Numerical answer
[src]
x1 = 93.4623814442964
x2 = 30.6305283725005
x3 = 87.1791961371168
x4 = -90.3207887907066
x5 = -7.06858347057703
x6 = 60.4756585816035
x7 = -51.0508806208341
x8 = -95.0331777710912
x9 = -101.316363078271
x10 = -50988.8341659257
x11 = 43.1968989868597
x12 = -88.7499924639117
x13 = -96.6039740978861
x14 = -44.7676953136546
x15 = -71.4712328691678
x16 = 73.0420291959627
x17 = 68.329640215578
x18 = -19.6349540849362
x19 = -84.037603483527
x20 = 66.7588438887831
x21 = -13.3517687777566
x22 = -38.484510006475
x23 = -14.9225651045515
x24 = -371.493331286993
x25 = 85.6083998103219
x26 = -82.4668071567321
x27 = -65.1880475619882
x28 = -46.3384916404494
x29 = 91.8915851175014
x30 = -27.4889357189107
x31 = -77.7544181763474
x32 = 11.7809724509617
x33 = 55.7632696012188
x34 = -63.6172512351933
x35 = -52.621676947629
x36 = -57.3340659280137
x37 = -58.9048622548086
x38 = -8.63937979737193
x39 = 99.7455667514759
x40 = -21.2057504117311
x41 = 24.3473430653209
x42 = 47.9092879672443
x43 = 10.2101761241668
x44 = 18.0641577581413
x45 = -704.502152567511
x46 = 41.6261026600648
x47 = 22.776546738526
x48 = 74.6128255227576
x49 = 16.4933614313464
x50 = 49.4800842940392
x51 = 652.665873783279
x52 = -40.0553063332699
x53 = 79.3252145031423
x54 = -33.7721210260903
x55 = 3.92699081698724
x56 = -76.1836218495525
x57 = -128.019900633784
x58 = -0.785398163397448
x59 = -69.9004365423729
x60 = 54.1924732744239
x61 = 5.49778714378214
x62 = 36.9137136796801
x63 = 29.0597320457056
x64 = -830.165858711103
x65 = 35.3429173528852
x66 = -25.9181393921158
x67 = 62.0464549083984
x68 = 80.8960108299372
x69 = -2.35619449019234
x70 = -32.2013246992954
x71 = 98.174770424681
x71 = 98.174770424681
The graph