Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation x^2+4*x+3=0
-
Equation 0,6(x-2)+4,6=0,4(7+x)
-
Equation x+2=0
-
Equation cos(x)=-2/3
- Express {x} in terms of y where:
- -2*x+2*y=4
- 10*x+3*y=2
- 8*x-9*y=-1
- -9*x-6*y=12
- Derivative of:
-
cos(x)
- -2/3
- Graphing y =:
-
cos(x)
- Integral of d{x}:
-
cos(x)
-
-2/3
- Limit of the function:
-
-2/3
-
Identical expressions
- cos(x)=- two / three
- co sinus of e of (x) equally minus 2 divide by 3
- co sinus of e of (x) equally minus two divide by three
- cosx=-2/3
- cos(x)=-2 divide by 3
-
Similar expressions
- cos(x)=+2/3
- cosx=1
- (2x+3)/4-(3x-2)/3=11/12
- cosx=-2/3
cos(x)=-2/3 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\cos{\left(x \right)} = - \frac{2}{3}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{acos}{\left(- \frac{2}{3} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(- \frac{2}{3} \right)}$$
Or
$$x = \pi n + \operatorname{acos}{\left(- \frac{2}{3} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(- \frac{2}{3} \right)}$$
, where n - is a integer
$$\cos{\left(x \right)} = - \frac{2}{3}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{acos}{\left(- \frac{2}{3} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(- \frac{2}{3} \right)}$$
Or
$$x = \pi n + \operatorname{acos}{\left(- \frac{2}{3} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(- \frac{2}{3} \right)}$$
, where n - is a integer
Rapid solution
[src]
x1 = -acos(-2/3) + 2*pi
$$x_{1} = - \operatorname{acos}{\left(- \frac{2}{3} \right)} + 2 \pi$$
x2 = acos(-2/3)
$$x_{2} = \operatorname{acos}{\left(- \frac{2}{3} \right)}$$
x2 = acos(-2/3)
Sum and product of roots
[src]
sum
-acos(-2/3) + 2*pi + acos(-2/3)
$$\operatorname{acos}{\left(- \frac{2}{3} \right)} + \left(- \operatorname{acos}{\left(- \frac{2}{3} \right)} + 2 \pi\right)$$
=
2*pi
$$2 \pi$$
product
(-acos(-2/3) + 2*pi)*acos(-2/3)
$$\left(- \operatorname{acos}{\left(- \frac{2}{3} \right)} + 2 \pi\right) \operatorname{acos}{\left(- \frac{2}{3} \right)}$$
=
(-acos(-2/3) + 2*pi)*acos(-2/3)
$$\left(- \operatorname{acos}{\left(- \frac{2}{3} \right)} + 2 \pi\right) \operatorname{acos}{\left(- \frac{2}{3} \right)}$$
(-acos(-2/3) + 2*pi)*acos(-2/3)
Numerical answer
[src]
x1 = -3.98266132415772
x2 = 96.5483035907157
x3 = -91.9472556246719
x4 = -71.4155623619973
x5 = -41.6817731672352
x6 = 47.9649584744148
x7 = 85.6640703174923
x8 = -8.58370929020145
x9 = 90.2651182835361
x10 = -58.8491917476381
x11 = 3.98266132415772
x12 = 54.2481437815944
x13 = 77.6987476691769
x14 = 83.9819329763565
x15 = 65.1323770548177
x16 = -47.9649584744148
x17 = -96.5483035907157
x18 = 2.30052398302186
x19 = 73.0976997031332
x20 = -22.8322172456965
x21 = 39.9996358260994
x22 = 33.7164505189198
x23 = -60.531329088774
x24 = -21.1500799045606
x25 = -65.1323770548177
x26 = 71.4155623619973
x27 = 605.486313472262
x28 = -33.7164505189198
x29 = -29.1154025528761
x30 = 14.866894597381
x31 = -77.6987476691769
x32 = -2.30052398302186
x33 = 60.531329088774
x34 = 35.3985878600557
x35 = 8.58370929020145
x36 = -35.3985878600557
x37 = -85.6640703174923
x38 = 98.2304409318515
x39 = -66.8145143959536
x40 = -27.4332652117402
x41 = -90.2651182835361
x42 = -54.2481437815944
x43 = 79.3808850103128
x44 = -10.2658466313373
x45 = -46.282821133279
x46 = -16.5490319385169
x47 = 41.6817731672352
x48 = -98.2304409318515
x49 = 91.9472556246719
x50 = 52.5660064404586
x51 = 46.282821133279
x52 = -83.9819329763565
x53 = 16.5490319385169
x54 = 22.8322172456965
x55 = 29.1154025528761
x56 = -39.9996358260994
x57 = 66.8145143959536
x58 = 10.2658466313373
x59 = 27.4332652117402
x60 = -73.0976997031332
x61 = 58.8491917476381
x62 = 21.1500799045606
x63 = -52.5660064404586
x64 = -79.3808850103128
x65 = -14.866894597381
x65 = -14.866894597381
The graph