Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation x^3=27
-
Equation x^4+2*x^2-8=0
-
Equation cos(x)=2/3
-
Equation (x-11)^4=(x+3)^4
- Express {x} in terms of y where:
- 6*x+17*y=3
- 1*x+4*y=20
- 20*x+7*y=-9
- -17*x+18*y=10
- Integral of d{x}:
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cosx
- Derivative of:
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cosx
- Graphing y =:
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cosx
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Identical expressions
- cosx=-√ two / two
- co sinus of e of x equally minus √2 divide by 2
- co sinus of e of x equally minus √ two divide by two
- cosx=-√2 divide by 2
-
Similar expressions
- cos(x^2)=0
- cos(x)=-1/3
- cos(x)+1/2=0
- cos(x)=2/3
- cos2x=-(√2/2)
- cosx=+√2/2
cosx=-√2/2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
___
-\/ 2
cos(x) = -------
2
$$\cos{\left(x \right)} = \frac{\left(-1\right) \sqrt{2}}{2}$$
Detail solution
Given the equation
$$\cos{\left(x \right)} = \frac{\left(-1\right) \sqrt{2}}{2}$$
- this is the simplest trigonometric equation
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
$$\cos{\left(x \right)} = \frac{\left(-1\right) \sqrt{2}}{2}$$
- this is the simplest trigonometric equation
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
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
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
Numerical answer
[src]
x1 = -40.0553063332699
x2 = 27.4889357189107
x3 = -335.36501577071
x4 = 90.3207887907066
x5 = -66.7588438887831
x6 = 85.6083998103219
x7 = -29.0597320457056
x8 = -60.4756585816035
x9 = 14.9225651045515
x10 = -79.3252145031423
x11 = -35.3429173528852
x12 = -27.4889357189107
x13 = -14.9225651045515
x14 = -98.174770424681
x15 = 66.7588438887831
x16 = 33.7721210260903
x17 = 39349.2333843756
x18 = 255.254403104171
x19 = -46.3384916404494
x20 = -85.6083998103219
x21 = -8.63937979737193
x22 = -54.1924732744239
x23 = -71.4712328691678
x24 = 8.63937979737193
x25 = 58.9048622548086
x26 = 3.92699081698724
x27 = -21.2057504117311
x28 = 73.0420291959627
x29 = 40.0553063332699
x30 = 54.1924732744239
x31 = 16.4933614313464
x32 = -65.1880475619882
x33 = 60.4756585816035
x34 = -47.9092879672443
x35 = 29.0597320457056
x36 = 10.2101761241668
x37 = -91.8915851175014
x38 = -41.6261026600648
x39 = 84.037603483527
x40 = 96.6039740978861
x41 = 41.6261026600648
x42 = 2.35619449019234
x43 = -2.35619449019234
x44 = -96.6039740978861
x45 = -73.0420291959627
x46 = 71.4712328691678
x47 = 65.1880475619882
x48 = -10.2101761241668
x49 = 98.174770424681
x50 = 104.457955731861
x51 = -58.9048622548086
x52 = 77.7544181763474
x53 = 35.3429173528852
x54 = -84.037603483527
x55 = -16.4933614313464
x56 = -52.621676947629
x57 = 2584.745355741
x58 = -90.3207887907066
x59 = 46.3384916404494
x60 = 22.776546738526
x61 = -77.7544181763474
x62 = -33.7721210260903
x63 = 21.2057504117311
x64 = -3.92699081698724
x65 = -22.776546738526
x66 = 79.3252145031423
x67 = 47.9092879672443
x68 = 52.621676947629
x69 = 91.8915851175014
x69 = 91.8915851175014
The graph