Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation x^2+3x+2=0
- Equation x+y=5
-
Equation sin(x)=3
-
Equation x^2-11*x+30=0
- Express {x} in terms of y where:
- 6*x+17*y=-11
- -13*x+7*y=-15
- -14*x-8*y=20
- 9*x+14*y=-10
-
Identical expressions
- two cosx+√2= zero
- 2 co sinus of e of x plus √2 equally 0
- two co sinus of e of x plus √2 equally zero
- 2cosx+√2=O
-
Similar expressions
- 2cosx-√2=0
2cosx+√2=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$2 \cos{\left(x \right)} + \sqrt{2} = 0$$
- this is the simplest trigonometric equation
We get:
$$2 \cos{\left(x \right)} = - \sqrt{2}$$
The equation is transformed to
$$\cos{\left(x \right)} = - \frac{\sqrt{2}}{2}$$
This equation is transformed to
$$x = \pi n + \operatorname{acos}{\left(- \frac{\sqrt{2}}{2} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(- \frac{\sqrt{2}}{2} \right)}$$
Or
$$x = \pi n + \frac{3 \pi}{4}$$
$$x = \pi n - \frac{\pi}{4}$$
, where n - is a integer
$$2 \cos{\left(x \right)} + \sqrt{2} = 0$$
- this is the simplest trigonometric equation
Move sqrt(2) to right part of the equation
with the change of sign in sqrt(2)
We get:
$$2 \cos{\left(x \right)} = - \sqrt{2}$$
Divide both parts of the equation by 2
The equation is transformed to
$$\cos{\left(x \right)} = - \frac{\sqrt{2}}{2}$$
This equation is transformed to
$$x = \pi n + \operatorname{acos}{\left(- \frac{\sqrt{2}}{2} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(- \frac{\sqrt{2}}{2} \right)}$$
Or
$$x = \pi n + \frac{3 \pi}{4}$$
$$x = \pi n - \frac{\pi}{4}$$
, where n - is a integer
Rapid solution
[src]
3*pi
x1 = ----
4
$$x_{1} = \frac{3 \pi}{4}$$
5*pi
x2 = ----
4
$$x_{2} = \frac{5 \pi}{4}$$
x2 = 5*pi/4
Sum and product of roots
[src]
sum
3*pi 5*pi ---- + ---- 4 4
$$\frac{3 \pi}{4} + \frac{5 \pi}{4}$$
=
2*pi
$$2 \pi$$
product
3*pi 5*pi ----*---- 4 4
$$\frac{3 \pi}{4} \frac{5 \pi}{4}$$
=
2 15*pi ------ 16
$$\frac{15 \pi^{2}}{16}$$
15*pi^2/16
Numerical answer
[src]
x1 = 91.8915851175014
x2 = -60.4756585816035
x3 = -85.6083998103219
x4 = -52.621676947629
x5 = 98.174770424681
x6 = 85.6083998103219
x7 = -33.7721210260903
x8 = 52.621676947629
x9 = 39349.2333843756
x10 = -8.63937979737193
x11 = 90.3207887907066
x12 = 35.3429173528852
x13 = 10.2101761241668
x14 = -14.9225651045515
x15 = 255.254403104171
x16 = -79.3252145031423
x17 = -54.1924732744239
x18 = 22.776546738526
x19 = -96.6039740978861
x20 = -90.3207887907066
x21 = 29.0597320457056
x22 = 16.4933614313464
x23 = 8.63937979737193
x24 = 3.92699081698724
x25 = -91.8915851175014
x26 = -71.4712328691678
x27 = -46.3384916404494
x28 = -98.174770424681
x29 = -65.1880475619882
x30 = -41.6261026600648
x31 = -47.9092879672443
x32 = 79.3252145031423
x33 = 14.9225651045515
x34 = -335.36501577071
x35 = -3.92699081698724
x36 = -66.7588438887831
x37 = 46.3384916404494
x38 = -16.4933614313464
x39 = -2.35619449019234
x40 = -77.7544181763474
x41 = -29.0597320457056
x42 = 41.6261026600648
x43 = 77.7544181763474
x44 = 96.6039740978861
x45 = -35.3429173528852
x46 = -40.0553063332699
x47 = 73.0420291959627
x48 = 60.4756585816035
x49 = -84.037603483527
x50 = -27.4889357189107
x51 = -22.776546738526
x52 = 40.0553063332699
x53 = -73.0420291959627
x54 = -58.9048622548086
x55 = -10.2101761241668
x56 = 65.1880475619882
x57 = 71.4712328691678
x58 = 54.1924732744239
x59 = 47.9092879672443
x60 = 27.4889357189107
x61 = 21.2057504117311
x62 = 66.7588438887831
x63 = 2584.745355741
x64 = 2.35619449019234
x65 = -21.2057504117311
x66 = 84.037603483527
x67 = 58.9048622548086
x68 = 33.7721210260903
x69 = 104.457955731861
x69 = 104.457955731861