Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation cos(x)=-sqrt(2)/2
-
Equation 7+5x-2x^2=0
- Equation x/24+11/24=23/24
- Equation (-2cos²x+sinx+1)×log0,5(-0,8cosx)=0
- Express {x} in terms of y where:
- 5*x-5*y=20
- 8*x-7*y=-13
- 15*x-15*y=16
- 9*x+18*y=6
- Derivative of:
-
cos(x)
- Integral of d{x}:
-
cos(x)
- Graphing y =:
-
cos(x)
-
Identical expressions
- cos(x)=-sqrt(two)/ two
- co sinus of e of (x) equally minus square root of (2) divide by 2
- co sinus of e of (x) equally minus square root of (two) divide by two
- cos(x)=-√(2)/2
- cosx=-sqrt2/2
- cos(x)=-sqrt(2) divide by 2
-
Similar expressions
- cos(x+pi/3)=(-1)/sqrt(2)
- cos(x)=+sqrt(2)/2
- 2sinx=5cosx
- (-2cos²x+sinx+1)×log0,5(-0,8cosx)=0
- cos*((pi(4x+48))/4)=-(sqrt(2)/2)
- cosx=-sqrt(2)/2
cos(x)=-sqrt(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
$$x = 2 \pi n + \operatorname{acos}{\left(- \frac{\sqrt{2}}{2} \right)}$$
$$x = 2 \pi n - \pi + \operatorname{acos}{\left(- \frac{\sqrt{2}}{2} \right)}$$
Or
$$x = 2 \pi n + \frac{3 \pi}{4}$$
$$x = 2 \pi n - \frac{\pi}{4}$$
, 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
$$x = 2 \pi n + \operatorname{acos}{\left(- \frac{\sqrt{2}}{2} \right)}$$
$$x = 2 \pi n - \pi + \operatorname{acos}{\left(- \frac{\sqrt{2}}{2} \right)}$$
Or
$$x = 2 \pi n + \frac{3 \pi}{4}$$
$$x = 2 \pi n - \frac{\pi}{4}$$
, where n - is a integer
Sum and product of roots
[src]
sum
3*pi 5*pi ---- + ---- 4 4
$$\left(\frac{3 \pi}{4}\right) + \left(\frac{5 \pi}{4}\right)$$
=
2*pi
$$2 \pi$$
product
3*pi 5*pi ---- * ---- 4 4
$$\left(\frac{3 \pi}{4}\right) * \left(\frac{5 \pi}{4}\right)$$
=
2 15*pi ------ 16
$$\frac{15 \pi^{2}}{16}$$
Rapid solution
[src]
3*pi
x_1 = ----
4
$$x_{1} = \frac{3 \pi}{4}$$
5*pi
x_2 = ----
4
$$x_{2} = \frac{5 \pi}{4}$$
Numerical answer
[src]
x1 = -335.36501577071
x2 = -85.6083998103219
x3 = -90.3207887907066
x4 = 65.1880475619882
x5 = 40.0553063332699
x6 = 60.4756585816035
x7 = -35.3429173528852
x8 = 33.7721210260903
x9 = -22.776546738526
x10 = -66.7588438887831
x11 = -96.6039740978861
x12 = -71.4712328691678
x13 = 8.63937979737193
x14 = 14.9225651045515
x15 = -73.0420291959627
x16 = 73.0420291959627
x17 = -16.4933614313464
x18 = -84.037603483527
x19 = 66.7588438887831
x20 = -14.9225651045515
x21 = 90.3207887907066
x22 = 84.037603483527
x23 = 85.6083998103219
x24 = -65.1880475619882
x25 = -47.9092879672443
x26 = 71.4712328691678
x27 = 255.254403104171
x28 = 2584.745355741
x29 = -46.3384916404494
x30 = -3.92699081698724
x31 = 91.8915851175014
x32 = -27.4889357189107
x33 = -77.7544181763474
x34 = 52.621676947629
x35 = 104.457955731861
x36 = -98.174770424681
x37 = -29.0597320457056
x38 = -52.621676947629
x39 = -79.3252145031423
x40 = -58.9048622548086
x41 = -8.63937979737193
x42 = 46.3384916404494
x43 = -21.2057504117311
x44 = 47.9092879672443
x45 = 10.2101761241668
x46 = 39349.2333843756
x47 = 77.7544181763474
x48 = 96.6039740978861
x49 = 41.6261026600648
x50 = -10.2101761241668
x51 = 22.776546738526
x52 = 16.4933614313464
x53 = -91.8915851175014
x54 = -60.4756585816035
x55 = -41.6261026600648
x56 = 58.9048622548086
x57 = -54.1924732744239
x58 = 27.4889357189107
x59 = -40.0553063332699
x60 = 79.3252145031423
x61 = -33.7721210260903
x62 = 3.92699081698724
x63 = 54.1924732744239
x64 = 35.3429173528852
x65 = 29.0597320457056
x66 = 21.2057504117311
x67 = 2.35619449019234
x68 = -2.35619449019234
x69 = 98.174770424681
x69 = 98.174770424681
The graph